A187164 Number of 3-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 48, 342, 1056, 2370, 4464, 7518, 11712, 17226, 24240, 32934, 43488, 56082, 70896, 88110, 107904, 130458, 155952, 184566, 216480, 251874, 290928, 333822, 380736, 431850, 487344, 547398, 612192, 681906, 756720, 836814, 922368, 1013562, 1110576

Offset

1,2

Comments

Row 3 of A187162.

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

Empirical: a(n) = 30*n^3 - 60*n^2 + 24*n for n>1.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 6*x^2*(8 + 25*x - 4*x^2 + x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

(End)

Example

A solution for 2 X 2 X 2:
..0..0.....0..0
..1..2.....0..3

Crossrefs

Cf. A187162.

Sequence in context: A211755 A211504 A211766 * A110275 A348120 A160335

Adjacent sequences: A187161 A187162 A187163 * A187165 A187166 A187167

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved