Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Mar 05 2022 22:11:44
%S 0,96,1104,3984,9612,18888,32712,51984,77604,110472,151488,201552,
%T 261564,332424,415032,510288,619092,742344,880944,1035792,1207788,
%U 1397832,1606824,1835664,2085252,2356488,2650272,2967504,3309084,3675912,4068888
%N Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C Row 4 of A187162.
%H R. H. Hardin, <a href="/A187165/b187165.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 150*n^3 - 426*n^2 + 312*n - 48 for n>2.
%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F G.f.: 12*x^2*(8 + 60*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
%F (End)
%e A solution for 2 X 2 X 2:
%e ..2..0.....3..4
%e ..1..0.....0..0
%Y Cf. A187162.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2011