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A187167 Number of 6-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2

%I #14 Apr 20 2018 14:39:02

%S 0,240,9504,51504,148224,320328,588924,975216,1500408,2185704,3052308,

%T 4121424,5414256,6952008,8755884,10847088,13246824,15976296,19056708,

%U 22509264,26355168,30615624,35311836,40465008,46096344,52227048,58878324

%N Number of 6-step self-avoiding walks on an n X n X n cube summed over all starting positions.

%H R. H. Hardin, <a href="/A187167/b187167.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 3534*n^3 - 15366*n^2 + 19536*n - 7056 for n>4.

%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)

%F G.f.: 12*x^2*(20 + 712*x + 1244*x^2 - 144*x^3 - 110*x^4 + 37*x^5 + 8*x^6) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

%F (End)

%e A solution for 2 X 2 X 2:

%e ..0..6.....0..1

%e ..4..5.....3..2

%Y Row 6 of A187162.

%K nonn,walk

%O 1,2

%A _R. H. Hardin_, Mar 06 2011

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