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 A187170 Number of 9-step self-avoiding walks on a n X n X n cube summed over all starting positions. 2

%I

%S 0,0,167016,2013360,8227752,21274896,43422072,76964016,124223214,

%T 187527168,269203674,371580528,496985526,647746464,826191138,

%U 1034647344,1275442878,1550905536,1863363114,2215143408,2608574214,3045983328

%N Number of 9-step self-avoiding walks on a n X n X n cube summed over all starting positions.

%C Row 9 of A187162.

%H R. H. Hardin, <a href="/A187170/b187170.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 387966*n^3 - 2452704*n^2 + 4766544*n - 2833872 for n>7.

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

%F G.f.: 6*x^3*(27836 + 224216*x + 196068*x^2 - 37336*x^3 - 32904*x^4 + 4576*x^5 + 4625*x^6 + 836*x^7 + 49*x^8) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>11.

%F (End)

%Y Cf. A187162.

%K nonn,walk

%O 1,3

%A _R. H. Hardin_, Mar 06 2011

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Last modified November 30 12:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)