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%I #13 Mar 05 2022 22:11:36
%S 0,48,342,1056,2370,4464,7518,11712,17226,24240,32934,43488,56082,
%T 70896,88110,107904,130458,155952,184566,216480,251874,290928,333822,
%U 380736,431850,487344,547398,612192,681906,756720,836814,922368,1013562,1110576
%N Number of 3-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C Row 3 of A187162.
%H R. H. Hardin, <a href="/A187164/b187164.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 30*n^3 - 60*n^2 + 24*n for n>1.
%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F G.f.: 6*x^2*(8 + 25*x - 4*x^2 + x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F (End)
%e A solution for 2 X 2 X 2:
%e ..0..0.....0..0
%e ..1..2.....0..3
%Y Cf. A187162.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2011
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