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A187165 Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2

%I

%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

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Last modified May 27 08:12 EDT 2022. Contains 354096 sequences. (Running on oeis4.)