A187163 - OEIS

%I #24 Mar 05 2022 22:11:27

%S 0,24,108,288,600,1080,1764,2688,3888,5400,7260,9504,12168,15288,

%T 18900,23040,27744,33048,38988,45600,52920,60984,69828,79488,90000,

%U 101400,113724,127008,141288,156600,172980,190464,209088,228888,249900,272160

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

%C Row 2 of A187162.

%H R. H. Hardin, <a href="/A187163/b187163.txt">Table of n, a(n) for n = 1..50</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 6*n^3 - 6*n^2.

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

%F G.f.: 12*x^2*(2 + x) / (1 - x)^4.

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

%F (End)

%F a(n) = 12 * A006002(n-1). - _Alois P. Heinz_, Feb 28 2022

%e A solution for 2 X 2 X 2:

%e   0  0     0  0

%e   1  0     2  0

%Y Cf. A006002, A187162.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, Mar 06 2011