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A187163
Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.
2
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
1,2
COMMENTS
Row 2 of A187162.
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
EXAMPLE
A solution for 2 X 2 X 2:
0 0 0 0
1 0 2 0
CROSSREFS
Sequence in context: A305950 A060334 A271915 * A211577 A101862 A211591
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 06 2011
STATUS
approved