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
Examples
A solution for 2 X 2 X 2: ..5..0.....4..1 ..0..0.....3..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..50
Crossrefs
Cf. A187162.
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)
Comments