A187166 Number of 5-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 144, 3240, 14256, 37470, 77184, 137754, 223536, 338886, 488160, 675714, 905904, 1183086, 1511616, 1895850, 2340144, 2848854, 3426336, 4076946, 4805040, 5614974, 6511104, 7497786, 8579376, 9760230, 11044704, 12437154, 13941936, 15563406

Offset

1,2

Comments

Row 5 of A187162.

Links

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

Formula

Empirical: a(n) = 726*n^3 - 2640*n^2 + 2688*n - 720 for n>3.

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

G.f.: 6*x^2*(24 + 444*x + 360*x^2 - 115*x^3 + 4*x^4 + 9*x^5) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

(End)

Example

A solution for 2 X 2 X 2:
..5..0.....4..1
..0..0.....3..2

Crossrefs

Cf. A187162.

Sequence in context: A223300 A330837 A252182 * A231836 A268968 A253134

Adjacent sequences: A187163 A187164 A187165 * A187167 A187168 A187169

Keyword

nonn,walk

Author

R. H. Hardin, Mar 06 2011

Status

approved