cp's OEIS Frontend

A188152 Number of 7-step self-avoiding walks on an n X n square summed over all starting positions.

%I A188152 #14 Apr 27 2018 09:22:39
%S A188152 0,0,112,1248,4152,8752,14932,22672,31972,42832,55252,69232,84772,
%T A188152 101872,120532,140752,162532,185872,210772,237232,265252,294832,
%U A188152 325972,358672,392932,428752,466132,505072,545572,587632,631252,676432,723172,771472
%N A188152 Number of 7-step self-avoiding walks on an n X n square summed over all starting positions.
%C A188152 Row 7 of A188147.
%H A188152 R. H. Hardin, <a href="/A188152/b188152.txt">Table of n, a(n) for n = 1..50</a>
%F A188152 Empirical: a(n) = 780*n^2 - 3960*n + 4432 for n>5.
%F A188152 Conjectures from _Colin Barker_, Apr 27 2018: (Start)
%F A188152 G.f.: 4*x^3*(28 + 228*x + 186*x^2 - 18*x^3 - 29*x^4 - 5*x^5) / (1 - x)^3.
%F A188152 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A188152 (End)
%e A188152 Some solutions for 3 X 3:
%e A188152   5 4 3   0 6 7   2 3 4   6 7 0   0 7 0   7 4 3   1 0 0
%e A188152   6 0 2   4 5 0   1 0 5   5 2 1   1 6 5   6 5 2   2 7 6
%e A188152   7 0 1   3 2 1   0 7 6   4 3 0   2 3 4   0 0 1   3 4 5
%Y A188152 Cf. A188147.
%K A188152 nonn
%O A188152 1,3
%A A188152 _R. H. Hardin_, Mar 22 2011