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

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 3 of A187162.

Examples

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

Links

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

Crossrefs

Cf. A187162.

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)