cp's OEIS Frontend

A188155 Number of 10-step self-avoiding walks on an n X n square summed over all starting positions.

%I A188155 #11 Apr 27 2018 09:22:51
%S A188155 0,0,0,3696,26000,82032,175312,303328,464304,657848,883928,1142544,
%T A188155 1433696,1757384,2113608,2502368,2923664,3377496,3863864,4382768,
%U A188155 4934208,5518184,6134696,6783744,7465328,8179448,8926104,9705296,10517024
%N A188155 Number of 10-step self-avoiding walks on an n X n square summed over all starting positions.
%C A188155 Row 10 of A188147.
%H A188155 R. H. Hardin, <a href="/A188155/b188155.txt">Table of n, a(n) for n = 1..50</a>
%F A188155 Empirical: a(n) = 16268*n^2 - 115548*n + 186528 for n>8.
%F A188155 Conjectures from _Colin Barker_, Apr 27 2018: (Start)
%F A188155 G.f.: 8*x^4*(462 + 1864*x + 1890*x^2 + 440*x^3 - 314*x^4 - 222*x^5 - 49*x^6 - 4*x^7) / (1 - x)^3.
%F A188155 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
%F A188155 (End)
%e A188155 Some solutions for 4 X 4:
%e A188155 ..0..8..9.10....0..7..8..9....0..3..4..5....0..0..6..7....1..0..0.10
%e A188155 ..0..7..6..1....0..6..5.10....1..2..7..6....0..4..5..8....2..7..8..9
%e A188155 ..0..0..5..2....0..3..4..0...10..9..8..0....0..3..2..9....3..6..0..0
%e A188155 ..0..0..4..3....0..2..1..0....0..0..0..0....0..0..1.10....4..5..0..0
%Y A188155 Cf. A188147.
%K A188155 nonn
%O A188155 1,4
%A A188155 _R. H. Hardin_, Mar 22 2011