cp's OEIS Frontend

A188153 Number of 8-step self-avoiding walks on an n X n square summed over all starting positions.

%I A188153 #13 Apr 27 2018 09:22:45
%S A188153 0,0,112,1976,8160,19312,35024,55104,79528,108296,141408,178864,
%T A188153 220664,266808,317296,372128,431304,494824,562688,634896,711448,
%U A188153 792344,877584,967168,1061096,1159368,1261984,1368944,1480248,1595896,1715888,1840224
%N A188153 Number of 8-step self-avoiding walks on an n X n square summed over all starting positions.
%C A188153 Row 8 of A188147.
%H A188153 R. H. Hardin, <a href="/A188153/b188153.txt">Table of n, a(n) for n = 1..50</a>
%F A188153 Empirical: a(n) = 2172*n^2 - 12500*n + 16096 for n>6.
%F A188153 Conjectures from _Colin Barker_, Apr 27 2018: (Start)
%F A188153 G.f.: 8*x^3*(2 + x)*(7 + 99*x + 111*x^2 - 15*x^3 - 18*x^4 - 3*x^5) / (1 - x)^3.
%F A188153 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
%F A188153 (End)
%e A188153 Some solutions for 4 X 4:
%e A188153   0 0 0 0    0 7 8 0    1 4 5 0    6 7 8 0    6 7 0 0
%e A188153   8 7 6 1    0 6 3 2    2 3 6 7    5 4 0 0    5 8 0 0
%e A188153   0 0 5 2    0 5 4 1    0 0 0 8    0 3 0 0    4 0 0 0
%e A188153   0 0 4 3    0 0 0 0    0 0 0 0    1 2 0 0    3 2 1 0
%Y A188153 Cf. A188147.
%K A188153 nonn
%O A188153 1,3
%A A188153 _R. H. Hardin_, Mar 22 2011