A187168 - OEIS

%I #14 Mar 05 2022 22:11:52

%S 0,192,25344,177120,568248,1298016,2466510,4175136,6525450,9619008,

%T 13557366,18442080,24374706,31456800,39789918,49475616,60615450,

%U 73310976,87663750,103775328,121747266,141681120,163678446,187840800,214269738

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

%C Row 7 of A187162.

%H R. H. Hardin, <a href="/A187168/b187168.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.

%F Conjectures from _Colin Barker_, Apr 21 2018: (Start)

%F 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 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.

%F (End)

%e A solution for 3 X 3 X 3:

%e ..0..0..0.....0..0..0.....0..0..0

%e ..0..0..0.....1..2..0.....0..0..0

%e ..7..0..0.....6..3..0.....5..4..0

%Y Cf. A187162.

%K nonn,walk

%O 1,2

%A _R. H. Hardin_, Mar 06 2011