cp's OEIS Frontend

A187168 Number of 7-step self-avoiding walks on an n X n X n cube summed over all starting positions.

%I A187168 #14 Mar 05 2022 22:11:52
%S A187168 0,192,25344,177120,568248,1298016,2466510,4175136,6525450,9619008,
%T A187168 13557366,18442080,24374706,31456800,39789918,49475616,60615450,
%U A187168 73310976,87663750,103775328,121747266,141681120,163678446,187840800,214269738
%N A187168 Number of 7-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C A187168 Row 7 of A187162.
%H A187168 R. H. Hardin, <a href="/A187168/b187168.txt">Table of n, a(n) for n = 1..50</a>
%F A187168 Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.
%F A187168 Conjectures from _Colin Barker_, Apr 21 2018: (Start)
%F A187168 G.f.: 6*x^2*(32 + 4096*x + 12816*x^2 + 1844*x^3 - 2240*x^4 + 133*x^5 + 220*x^6 + 25*x^7) / (1 - x)^4.
%F A187168 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.
%F A187168 (End)
%e A187168 A solution for 3 X 3 X 3:
%e A187168 ..0..0..0.....0..0..0.....0..0..0
%e A187168 ..0..0..0.....1..2..0.....0..0..0
%e A187168 ..7..0..0.....6..3..0.....5..4..0
%Y A187168 Cf. A187162.
%K A187168 nonn,walk
%O A187168 1,2
%A A187168 _R. H. Hardin_, Mar 06 2011