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

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn
• walk

Examples

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

Links

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

Crossrefs

Row 6 of A187162.

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)