A187167 Number of 6-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 240, 9504, 51504, 148224, 320328, 588924, 975216, 1500408, 2185704, 3052308, 4121424, 5414256, 6952008, 8755884, 10847088, 13246824, 15976296, 19056708, 22509264, 26355168, 30615624, 35311836, 40465008, 46096344, 52227048, 58878324

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3534*n^3 - 15366*n^2 + 19536*n - 7056 for n>4.

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

G.f.: 12*x^2*(20 + 712*x + 1244*x^2 - 144*x^3 - 110*x^4 + 37*x^5 + 8*x^6) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

Example

A solution for 2 X 2 X 2:
..0..6.....0..1
..4..5.....3..2

Crossrefs

Row 6 of A187162.

Sequence in context: A008340 A252183 A251434 * A282227 A268902 A232994

Adjacent sequences: A187164 A187165 A187166 * A187168 A187169 A187170

Keyword

nonn,walk

Author

R. H. Hardin, Mar 06 2011

Status

approved