cp's OEIS Frontend

A187163 Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.

%I A187163 #24 Mar 05 2022 22:11:27
%S A187163 0,24,108,288,600,1080,1764,2688,3888,5400,7260,9504,12168,15288,
%T A187163 18900,23040,27744,33048,38988,45600,52920,60984,69828,79488,90000,
%U A187163 101400,113724,127008,141288,156600,172980,190464,209088,228888,249900,272160
%N A187163 Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C A187163 Row 2 of A187162.
%H A187163 R. H. Hardin, <a href="/A187163/b187163.txt">Table of n, a(n) for n = 1..50</a>
%H A187163 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A187163 a(n) = 6*n^3 - 6*n^2.
%F A187163 From _Colin Barker_, Apr 20 2018: (Start)
%F A187163 G.f.: 12*x^2*(2 + x) / (1 - x)^4.
%F A187163 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A187163 (End)
%F A187163 a(n) = 12 * A006002(n-1). - _Alois P. Heinz_, Feb 28 2022
%e A187163 A solution for 2 X 2 X 2:
%e A187163   0  0     0  0
%e A187163   1  0     2  0
%Y A187163 Cf. A006002, A187162.
%K A187163 nonn,easy
%O A187163 1,2
%A A187163 _R. H. Hardin_, Mar 06 2011