This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A336818 #28 Feb 21 2021 02:08:54 %S A336818 4,8,4,8,12,4,8,32,12,4,8,64,36,12,4,8,104,96,36,12,4,8,176,240,100, %T A336818 36,12,4,8,296,520,280,100,36,12,4,0,496,1048,728,284,100,36,12,4,0, %U A336818 848,2104,1816,776,184,100,36,12,4,0,1392,4168,4176,2112,780,284,100,36,12,4 %N A336818 Table read by antidiagonals: T(b,n) is the number of n-step self avoiding walks on a 2D square grid confined inside a square box of size 2b X 2b where the walk starts at the middle of the box. %H A336818 A. R. Conway et al., <a href="http://dx.doi.org/10.1088/0305-4470/26/7/012">Algebraic techniques for enumerating self-avoiding walks on the square lattice</a>, J. Phys A 26 (1993) 1519-1534. %H A336818 A. J. Guttmann and A. R. Conway, <a href="http://dx.doi.org/10.1007/PL00013842">Self-Avoiding Walks and Polygons</a>, Annals of Combinatorics 5 (2001) 319-345. %F A336818 For n <= b, T(b,n) = A001411(n). %F A336818 For n >= b^2, T(b,n) = 0 as the walks have more steps than there are free grid points inside the box. %e A336818 T(1,3) = 8. The one 3-step walk taking a first step to the right followed by a step upward is: %e A336818 . %e A336818 +--+ %e A336818 | %e A336818 *--+ %e A336818 . %e A336818 This walk can take a downward second step, and also have a first step in the four possible directions, given a total of 1*2*4 = 8 total walks. %e A336818 . %e A336818 The table begins: %e A336818 . %e A336818 4 8 8 8 8 8 8 8 0 0 0 0 0 0 0... %e A336818 4 12 32 64 104 176 296 496 848 1392 2280 3624 5472 8200 10920... %e A336818 4 12 36 96 240 520 1048 2104 4168 8288 16488 32536 64680 126560 248328... %e A336818 4 12 36 100 280 728 1816 4176 9304 20400 44216 95680 206104 442984 953720... %e A336818 4 12 36 100 284 776 2112 5448 13704 32824 77232 178552 409144 932152 2113736... %e A336818 4 12 36 100 284 780 2168 5848 15672 40472 102816 252992 615328 1472808 3501200... %e A336818 4 12 36 100 284 780 2172 5912 16192 43360 115328 298856 765864 1919328 4770784... %e A336818 4 12 36 100 284 780 2172 5916 16264 44016 119392 318328 843848 2194920 5664648... %e A336818 4 12 36 100 284 780 2172 5916 16268 44096 120200 323856 872920 2321600 6146400... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120288 324832 880232 2363520 6344240... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120292 324928 881392 2372968 6402928... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881496 2374328 6414896... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374440 6416472... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374444 6416592... %e A336818 4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374444 6416596... %e A336818 ... %Y A336818 Cf. A001411 (b->infinity), A336872 (start on edge of box), A116903, A038373. %K A336818 nonn,walk,tabl %O A336818 1,1 %A A336818 _Scott R. Shannon_, Aug 06 2020