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%I #14 Apr 27 2018 09:22:33
%S 0,0,128,800,2112,4008,6472,9504,13104,17272,22008,27312,33184,39624,
%T 46632,54208,62352,71064,80344,90192,100608,111592,123144,135264,
%U 147952,161208,175032,189424,204384,219912,236008,252672,269904,287704,306072
%N Number of 6-step self-avoiding walks on an n X n square summed over all starting positions.
%C Row 6 of A188147.
%H R. H. Hardin, <a href="/A188151/b188151.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 284*n^2 - 1228*n + 1152 for n>4.
%F Conjectures from _Colin Barker_, Apr 27 2018: (Start)
%F G.f.: 8*x^3*(16 + 52*x + 12*x^2 - 7*x^3 - 2*x^4) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%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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