﻿ 3N+C SEQUENCE LOOPS
```		 3N+C SEQUENCE LOOPS, ONE ATTACHMENT POINT

The loops are classified into types A, B, and C (to be defined in the
following).  Type A occurs 12 times, type B occurs 7 times, and type C
occurs 45 times.  Sequence vectors of the segments are given.

Type A (last odd element less than order/6, doesn't determine order)

c=-23, n=31, order=98304
12589<order/6, 3153,9436, count=36
(50448 25224 12612 6306 3153 9436 4718 2359 7054 3527 10558 5279
15814 7907 23698 11849 35524 17762 8881 26620 13310 6655 19942 9971
29890 14945 44812 22406 11203 33586 16793 50356 25178 12589 37744 18872
9436)
sv=(4, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 3)

c=-23, n=31, order=98304
12077<order/6, 4041->3025,9052, count=39
(64656 32328 16164 8082 4041 12100 6050 3025 9052 4526 2263 6766
3383 10126 5063 15166 7583 22726 11363 34066 17033 51076 25538 12769
38284 19142 9571 28690 14345 43012 21506 10753 32236 16118 8059 24154
12077 36208 18104 9052)
sv=(4, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 3)

c=37, n=9, order=384
49<order/6, 3,46, count=16
(192 96 48 24 12 6 3 46 23 106 53 196 98 49 184
92 46)
sv=(6, 1, 1, 2, 3)

c=71, n=44, order=196608
30275<order/6, 7551,22724, count=49
(120816 60408 30204 15102 7551 22724 11362 5681 17114 8557
25742 12871 38684 19342 9671 29084 14542 7271 21884 10942
5471 16484 8242 4121 12434 6217 18722 9361 28154 14077
42302 21151 63524 31762 15881 47714 23857 71642 35821 107534
53767 161372 80686 40343 121100 60550 30275 90896 45448 22724)
sv=(4, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3)

c=-77, n=36, order=49152
5191<order/6, 1317,3874, count=42
(42144 21072 10536 5268 2634 1317 3874 1937 5734 2867 8524 4262 2131
6316 3158 1579 4660 2330 1165 3418 1709 5050 2525 7498 3749 11170
5585 16678 8339 24940 12470 6235 18628 9314 4657 13894 6947 20764 10382
5191 15496 7748 3874)
sv=(5, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3)

c=-95, n=28, order=12288
1933<order/6, 507,1426, count=33
(8112 4056 2028 1014 507 1426 713 2044 1022 511 1438 719 2062
1031 2998 1499 4402 2201 6508 3254 1627 4786 2393 7084 3542 1771
5218 2609 7732 3866 1933 5704 2852 1426)
sv=(4, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3)

c=-119, n=30, order=6144
869<order/6, 369->247,622, count=38
(5904 2952 1476 738 369 988 494 247 622 311 814
407 1102 551 1534 767 2182 1091 3154 1577 4612 2306
1153 3340 1670 835 2386 1193 3460 1730 865 2476 1238
619 1738 869 2488 1244 622)
sv=(4, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 3)

c=139, n=18, order=49152
8129<order/6, -2067,-6062, count=23
(-33072 -16536 -8268 -4134 -2067 -6062 -3031 -8954 -4477 -13292 -6646
-3323 -9830 -4915 -14606 -7303 -21770 -10885 -32516 -16258 -8129 -24248
-12124 -6062)
sv=(4, 1, 1, 2, 1, 1, 1, 2, 3)

c=139, n=18, order=49152
7265<order/6, -1851,-5414, count=23
(-29616 -14808 -7404 -3702 -1851 -5414 -2707 -7982 -3991 -11834 -5917
-17612 -8806 -4403 -13070 -6535 -19466 -9733 -29060 -14530 -7265 -21656
-10828 -5414)
sv=(4, 1, 1, 1, 2, 1, 1, 2, 3)

c=139, n=18, order=49152
7201<order/6, -2493->-1835,-5366, count=26
(-39888 -19944 -9972 -4986 -2493 -7340 -3670 -1835 -5366 -2683 -7910
-3955 -11726 -5863 -17450 -8725 -26036 -13018 -6509 -19388 -9694 -4847
-14402 -7201 -21464 -10732 -5366)
sv=(4, 2, 1, 1, 1, 1, 2, 2, 1, 3)

c=139, n=18, order=49152
6689<order/6, -1707,-4982, count=23
(-27312 -13656 -6828 -3414 -1707 -4982 -2491 -7334 -3667 -10862 -5431
-16154 -8077 -24092 -12046 -6023 -17930 -8965 -26756 -13378 -6689 -19928
-9964 -4982)
sv=(4, 1, 1, 1, 1, 2, 1, 2, 3)

c=139, n=18, order=49152
6305<order/6, -1611,-4694, count=23
(-25776 -12888 -6444 -3222 -1611 -4694 -2347 -6902 -3451 -10214 -5107
-15182 -7591 -22634 -11317 -33812 -16906 -8453 -25220 -12610 -6305 -18776
-9388 -4694)
sv=(4, 1, 1, 1, 1, 1, 2, 2, 3)

Type B (last odd element less than order/6, still determines order)

c=-5, n=4, order=12
1<order/6, 3->1,-2, count=9
(6 3 4 2 1 -2 -1 -8 -4 -2)
sv=(1, 2, 1, 3)

c=-13, n=5, order=24
1<order/6, 3,-4, count=8
(12 6 3 -4 -2 -1 -16 -8 -4)
sv=(2, 2, 3)

c=23, n=7, order=96
11<order/6, -3,14, count=12
(-48 -24 -12 -6 -3 14 7 44 22 11 56 28 14)
sv=(4, 1, 2, 3)

c=55, n=8, order=192
19<order/6, -9,28, count=13
(-144 -72 -36 -18 -9 28 14 7 76 38 19 112 56 28)
sv=(4, 2, 2, 3)

c=91, n=18, order=768
127<order/6, 9,118, count=25
(576 288 144 72 36 18 9 118 59 268 134 67 292
146 73 310 155 556 278 139 508 254 127 472 236 118)
sv=(6, 1, 2, 2, 1, 2, 2, 3)

c=101, n=10, order=768
121<order/6, -27->5,116, count=18
(-432 -216 -108 -54 -27 20 10 5 116 58 29 188 94
47 242 121 464 232 116)
sv=(4, 2, 2, 2, 1, 3)

c=-115, n=4, order=192
23<order/6, 69->23,-46, count=9
(138 69 92 46 23 -46 -23 -184 -92 -46)
sv=(1, 2, 1, 3)

TYPE C (last odd element greater than order/6)

c=-1, n=18, order=384
91>order/6, 21->23,68, count=28 (second of pair)
(336 168 84 42 21 62 31 92 46 23 68 34 17
50 25 74 37 110 55 164 82 41 122 61 182 91
272 136 68)
sv=(4, 1, 2, 2, 1, 1, 1, 2, 1, 1, 3)

c=5, n=8, order=192
49>order/6, 3->11,38, count=21
(96 48 24 12 6 3 14 7 26 13 44 22 11
38 19 62 31 98 49 152 76 38)
sv=(5, 1, 1, 2, 1, 1, 1, 3)

c=7, n=6, order=48
11>order/6, -3->1,10, count=15
(-24 -12 -6 -3 -2 -1 4 2 1 10 5 22 11
40 20 10)
sv=(3, 1, 2, 1, 1, 3)

c=13, n=13, order=3072
601>order/6, 147,454, count=18
(2352 1176 588 294 147 454 227 694 347 1054 527 1594 797
2404 1202 601 1816 908 454)
sv=(4, 1, 1, 1, 1, 2, 3)

c=13, n=13, order=3072
665>order/6, 213->163,502, count=20
(1704 852 426 213 652 326 163 502 251 766 383 1162 581
1756 878 439 1330 665 2008 1004 502)
sv=(3, 2, 1, 1, 1, 2, 1, 3)

c=13, n=13, order=3072
761>order/6, 159->187,574, count=23
(2544 1272 636 318 159 490 245 748 374 187 574 287 874
437 1324 662 331 1006 503 1522 761 2296 1148 574)
sv=(4, 1, 2, 1, 1, 2, 1, 1, 3)

c=13, n=13, order=3072
905>order/6, 123->223,682, count=25
(1968 984 492 246 123 382 191 586 293 892 446 223 682
341 1036 518 259 790 395 1198 599 1810 905 2728 1364 682)
sv=(4, 1, 1, 2, 1, 2, 1, 1, 1, 3)

c=13, n=13, order=6144
1121>order/6, 99->277,844, count=28
(3168 1584 792 396 198 99 310 155 478 239 730 365 1108
554 277 844 422 211 646 323 982 491 1486 743 2242 1121
3376 1688 844)
sv=(5, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3)

c=-17, n=10, order=768
179>order/6, 33->49,130, count=24
(528 264 132 66 33 82 41 106 53 142 71
196 98 49 130 65 178 89 250 125 358 179
520 260 130)
sv=(2, 1, 1, 1, 1, 3)

c=-23, n=31, order=49152
9781>order/6, 2451,7330, count=36
(39216 19608 9804 4902 2451 7330 3665 10972 5486 2743 8206 4103
12286 6143 18406 9203 27586 13793 41356 20678 10339 30994 15497 46468
23234 11617 34828 17414 8707 26098 13049 39124 19562 9781 29320 14660
7330)
sv=(4, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3)

c=23, n=7, order=96
19>order/6, -9->-1,20, count=14
(-72 -36 -18 -9 -4 -2 -1 20 10 5 38 19 80
40 20)
sv=(3, 2, 2, 1, 3)

c=25, n=12, order=192
37>order/6, 3,34, count=18
(96 48 24 12 6 3 34 17 76 38 19 82 41
148 74 37 136 68 34)
sv=(5, 1, 2, 1, 2, 3)

c=-29, n=20, order=1536
311>order/6, 123->85,226, count=27
(984 492 246 123 340 170 85 226 113 310 155
436 218 109 298 149 418 209 598 299 868 434
217 622 311 904 452 226)
sv=(3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3)

c=-31, n=15, order=1536
517>order/6, 63->137,380, count=31
(1008 504 252 126 63 158 79 206 103 278 139
386 193 548 274 137 380 190 95 254 127 350
175 494 247 710 355 1034 517 1520 760 380)
sv=(4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3)

c=35, n=12, order=384
79>order/6, 3->11,68, count=22
(192 96 48 24 12 6 3 44 22 11 68 34 17 86 43 164
82 41 158 79 272 136 68)
sv=(6, 2, 2, 1, 2, 1, 3)

c=37, n=9, order=384
65>order/6, -3->7,58, count=19
(-192 -96 -48 -24 -12 -6 -3 28 14 7 58 29 124 62 31
130 65 232 116 58)
sv=(6, 2, 1, 2, 1, 3)

c=37, n=9, order=384
89>order/6, -9->13,76, count=20
(-288 -144 -72 -36 -18 -9 10 5 52 26 13 76 38 19 94
47 178 89 304 152 76)
sv=(5, 1, 2, 2, 1, 1, 3)

c=47, n=11, order=768
179>order/6, 33,146, count=16
(528 264 132 66 33 146 73 266 133 446 223 716 358 179 584
292 146)
sv=(4, 1, 1, 1, 2, 3)

c=47, n=11, order=768
211>order/6, 39->41,170, count=19
(624 312 156 78 39 164 82 41 170 85 302 151 500 250 125
422 211 680 340 170)
sv=(4, 2, 1, 1, 2, 1, 3)

c=47, n=11, order=1536
259>order/6, 21->53,206, count=23
(1344 672 336 168 84 42 21 110 55 212 106 53 206 103 356
178 89 314 157 518 259 824 412 206)
sv=(6, 1, 2, 1, 2, 1, 1, 3)

c=47, n=11, order=1536
331>order/6, 9->71,260, count=26
(1152 576 288 144 72 36 18 9 74 37 158 79 284 142 71
260 130 65 242 121 410 205 662 331 1040 520 260)
sv=(7, 1, 1, 2, 2, 1, 1, 1, 3)

c=59, n=16, order=3072
967>order/6, 93->227,740, count=29
(2976 1488 744 372 186 93 338 169 566 283 908 454 227 740
370 185 614 307 980 490 245 794 397 1250 625 1934 967 2960
1480 740)
sv=(5, 1, 1, 2, 2, 1, 2, 1, 1, 1, 3)

c=59, n=16, order=3072
559>order/6, 147->125,434, count=24
(2352 1176 588 294 147 500 250 125 434 217 710 355 1124 562
281 902 451 1412 706 353 1118 559 1736 868 434)
sv=(4, 2, 1, 1, 2, 1, 2, 1, 3)

c=59, n=16, order=3072
775>order/6, 219->179,596, count=23
(1752 876 438 219 716 358 179 596 298 149 506 253 818 409
1286 643 1988 994 497 1550 775 2384 1192 596)
sv=(3, 2, 2, 1, 1, 1, 2, 1, 3)

c=71, n=15, order=768
131>order/6, 15,116, count=21
(480 240 120 60 30 15 116 58 29 158 79
308 154 77 302 151 524 262 131 464 232 116)
sv=(5, 2, 1, 2, 1, 2, 3)

c=101, n=10, order=384
65>order/6, -9,74, count=16
(-288 -144 -72 -36 -18 -9 74 37 212 106 53 260 130
65 296 148 74)
sv=(5, 1, 2, 2, 3)

c=101, n=10, order=384
89>order/6, -3,92, count=17
(-192 -96 -48 -24 -12 -6 -3 92 46 23 170 85 356
178 89 368 184 92)
sv=(6, 2, 1, 2, 3)

c=-115, n=12, order=3072
601>order/6, 147->179,422, count=28
(2352 1176 588 294 147 326 163 374 187 446 223
554 277 716 358 179 422 211 518 259 662 331
878 439 1202 601 1688 844 422)
sv=(4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3)

c=139, n=18, order=24576
7777>order/6, -2685->-1979,-5798, count=25
(-21480 -10740 -5370 -2685 -7916 -3958 -1979 -5798 -2899 -8558 -4279
-12698 -6349 -18908 -9454 -4727 -14042 -7021 -20924 -10462 -5231 -15554
-7777 -23192 -11596 -5798)
sv=(3, 2, 1, 1, 1, 2, 1, 2, 1, 3)

c=139, n=18, order=49152
15529>order/6, -1659->-3917,-11612, count=32
(-26544 -13272 -6636 -3318 -1659 -4838 -2419 -7118 -3559 -10538 -5269
-15668 -7834 -3917 -11612 -5806 -2903 -8570 -4285 -12716 -6358 -3179
-9398 -4699 -13958 -6979 -20798 -10399 -31058 -15529 -46448 -23224 -11612)
sv=(4, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 3)

c=139, n=18, order=49152
13801>order/6, -2163->-3485,-10316, count=30
(-34608 -17304 -8652 -4326 -2163 -6350 -3175 -9386 -4693 -13940 -6970
-3485 -10316 -5158 -2579 -7598 -3799 -11258 -5629 -16748 -8374 -4187
-12422 -6211 -18494 -9247 -27602 -13801 -41264 -20632 -10316)
sv=(4, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 3)

c=139, n=18, order=49152
13585>order/6, -1467->-3431,-10154, count=33
(-46944 -23472 -11736 -5868 -2934 -1467 -4262 -2131 -6254 -3127 -9242
-4621 -13724 -6862 -3431 -10154 -5077 -15092 -7546 -3773 -11180 -5590
-2795 -8246 -4123 -12230 -6115 -18206 -9103 -27170 -13585 -40616 -20308
-10154)
sv=(5, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 3)

c=139, n=18, order=49152
11881>order/6, -4053->-3005,-8876, count=25
(-32424 -16212 -8106 -4053 -12020 -6010 -3005 -8876 -4438 -2219 -6518
-3259 -9638 -4819 -14318 -7159 -21338 -10669 -31868 -15934 -7967 -23762
-11881 -35504 -17752 -8876)
sv=(3, 2, 2, 1, 1, 1, 1, 2, 1, 3)

c=139, n=18, order=49152
11857>order/6, -1875->-2999,-8858, count=30
(-30000 -15000 -7500 -3750 -1875 -5486 -2743 -8090 -4045 -11996 -5998
-2999 -8858 -4429 -13148 -6574 -3287 -9722 -4861 -14444 -7222 -3611
-10694 -5347 -15902 -7951 -23714 -11857 -35432 -17716 -8858)
sv=(4, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3)

c=139, n=18, order=49152
11369>order/6, -2877,-8492, count=23
(-46032 -23016 -11508 -5754 -2877 -8492 -4246 -2123 -6230 -3115 -9206
-4603 -13670 -6835 -20366 -10183 -30410 -15205 -45476 -22738 -11369 -33968
-16984 -8492)
sv=(4, 2, 1, 1, 1, 1, 1, 2, 3)

c=139, n=18, order=49152
10705>order/6, -2487->-2711,-7994, count=28
(-39792 -19896 -9948 -4974 -2487 -7322 -3661 -10844 -5422 -2711 -7994
-3997 -11852 -5926 -2963 -8750 -4375 -12986 -6493 -19340 -9670 -4835
-14366 -7183 -21410 -10705 -31976 -15988 -7994)
sv=(4, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3)

c=139, n=18, order=49152
10561>order/6, -1683->02675,-7886, count=30
(-26928 -13464 -6732 -3366 -1683 -4910 -2455 -7226 -3613 -10700 -5350
-2675 -7886 -3943 -11690 -5845 -17396 -8698 -4349 -12908 -6454 -3227
-9542 -4771 -14174 -7087 -21122 -10561 -31544 -15772 -7886)
sv=(4, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3)

c=139, n=18, order=49152
9937>order/6, -3405->-2519,-7418, count=25
(-27240 -13620 -6810 -3405 -10076 -5038 -2519 -7418 -3709 -10988 -5494
-2747 -8102 -4051 -12014 -6007 -17882 -8941 -26684 -13342 -6671 -19874
-9937 -29672 -14836 -7418)
sv=(3, 2, 1, 2, 1, 1, 1, 2, 1, 3)

c=139, n=18, order=49152
9425>order/6, -2391,-7034, count=23
(-38256 -19128 -9564 -4782 -2391 -7034 -3517 -10412 -5206 -2603 -7670
-3835 -11366 -5683 -16910 -8455 -25226 -12613 -37700 -18850 -9425 -28136
-14068 -7034)
sv=(4, 1, 2, 1, 1, 1, 1, 2, 3)

c=139, n=18, order=49152
9409>order/6, -2199->-2387,-7022, count=28
(-35184 -17592 -8796 -4398 -2199 -6458 -3229 -9548 -4774 -2387 -7022
-3511 -10394 -5197 -15452 -7726 -3863 -11450 -5725 -17036 -8518 -4259
-12638 -6319 -18818 -9409 -28088 -14044 -7022)
sv=(4, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3)

c=139, n=18, order=49152
8641>order/6, -2973->-2195,-6446, count=26
(-47568 -23784 -11892 -5946 -2973 -8780 -4390 -2195 -6446 -3223 -9530
-4765 -14156 -7078 -3539 -10478 -5239 -15578 -7789 -23228 -11614 -5807
-17282 -8641 -25784 -12892 -6446)
sv=(4, 2, 1, 1, 2, 1, 1, 2, 1, 3)

c=139, n=18, order=49152
8545>order/6, -2007->-2171,-6374, count=28
(-32112 -16056 -8028 -4014 -2007 -5882 -2941 -8684 -4342 -2171 -6374
-3187 -9422 -4711 -13994 -6997 -20852 -10426 -5213 -15500 -7750 -3875
-11486 -5743 -17090 -8545 -25496 -12748 -6374)
sv=(4, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3)

c=139, n=18, order=98304
18121>order/6, -1323->-4565,-13556, count=36
(-84672 -42336 -21168 -10584 -5292 -2646 -1323 -3830 -1915 -5606 -2803
-8270 -4135 -12266 -6133 -18260 -9130 -4565 -13556 -6778 -3389 -10028
-5014 -2507 -7382 -3691 -10934 -5467 -16262 -8131 -24254 -12127 -36242
-18121 -54224 -27112 -13556)
sv=(6, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 3)

c=145, n=20, order=6144
1555>order/6, -615->-425,-1130, count=27
(-4920 -2460 -1230 -615 -1700 -850 -425 -1130 -565 -1550 -775
-2180 -1090 -545 -1490 -745 -2090 -1045 -2990 -1495 -4340 -2170
-1085 -3110 -1555 -4520 -2260 -1130)
sv=(3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3)

c=-163, n=18, order=49152
14833>order/6, 3423->3749,11084, count=27
(27384 13692 6846 3423 10106 5053 14996 7498 3749 11084 5542
2771 8150 4075 12062 6031 17930 8965 26732 13366 6683 19886
9943 29666 14833 44336 22168 11084)
sv=(3, 1, 2, 2, 1, 1, 1, 2, 1, 1, 3)
```