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