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

1,2

Comments

Row 2 of A187162.

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

Example

A solution for 2 X 2 X 2:
  0  0     0  0
  1  0     2  0

Crossrefs

Cf. A006002, A187162.

Sequence in context: A305950 A060334 A271915 * A211577 A101862 A211591

Adjacent sequences: A187160 A187161 A187162 * A187164 A187165 A187166

Keyword

nonn,easy

Author

R. H. Hardin, Mar 06 2011

Status

approved