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Number of N-Step Self-Avoiding Walks & Sum of Squares of Their End-to-End Distances on Simple Cubic Lattice1

N cNSAW ρNSAW
0  1 0
1   6 6
1   30 72
3   150 582
4   726 4 032
5 3 534 25 556
6 16 926 153 528
7 81 390 886 926
8 387 966 4 983 456
9 1 853 886 27 401 502
10 8 809 878 148 157 880
11 41 934 150 790 096 950
12 198 842 742 4 166 321 184
13 943 974 510 21 760 624 254
14 4 468 911 678 11 274 379 663
15 21 175 146 054 580 052 260 230
16 100 121 875 974 2 966 294 589 312
17 473 730 252 102 15 087 996 161 382
18 2 237 723 684 094 76 384 144 381 272
19 10 576 033 219 614 385 066 579 325 550
20 49 917 327 838 734 1 933 885 653 380 544
21 235 710 090 502 158 9 679 153 967 272 734
22 1 111 781 983 442 406 48 295 148 145 655 224
23 5 245 988 215 191 414 240 292 643 254 616 694
24 24 730 180 885 580 790 1 192 504 522 283 625 600
25 116 618 841 700 433 358 5 904 015 201 226 909 614
26 549 493 796 867 100 942 29 166 829 902 019 914 840
1D. MacDonald, S. Joseph, D. L. Hunter, L. L. Moseley, N. Jan and A. J. Guttmann, J. Phys. A: Math. Gen., 33, 5973 (2000)
2K.Y. Lin and M. Chen, J. Phys. A: Math. Gen., 35, 1501–1508 (2002)
3R.D. Schram, G.T. Barkema, and R.H. Bisseling, J. Stat. Mech.: Theory and Experiment, 6, 06019 (2011)

Loop-Erased Walks

Analytical Method