A187163 Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.
0, 24, 108, 288, 600, 1080, 1764, 2688, 3888, 5400, 7260, 9504, 12168, 15288, 18900, 23040, 27744, 33048, 38988, 45600, 52920, 60984, 69828, 79488, 90000, 101400, 113724, 127008, 141288, 156600, 172980, 190464, 209088, 228888, 249900, 272160
Offset: 1
Examples
A solution for 2 X 2 X 2: 0 0 0 0 1 0 2 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..50
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Formula
a(n) = 6*n^3 - 6*n^2.
From Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(2 + x) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
a(n) = 12 * A006002(n-1). - Alois P. Heinz, Feb 28 2022
Comments