A187169 Number of 8-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 144, 67824, 608928, 2188608, 5299056, 10416624, 18026640, 28617228, 42676728, 60693480, 83155824, 110552100, 143370648, 182099808, 227227920, 279243324, 338634360, 405889368, 481496688, 565944660, 659721624, 763315920, 877215888

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn
• walk

Comments

Row 8 of A187162.

Examples

			A solution for 3 X 3 X 3:
..0..8..0.....2..7..0.....3..0..0
..0..0..0.....1..6..0.....4..5..0
..0..0..0.....0..0..0.....0..0..0
		

Links

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

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 81390*n^3 - 463074*n^2 + 801216*n - 418032 for n>6.

Conjectures from Colin Barker, Apr 21 2018: (Start)

G.f.: 12*x^2*(12 + 5604*x + 28208*x^2 + 13272*x^3 - 6080*x^4 - 1320*x^5 + 748*x^6 + 233*x^7 + 18*x^8) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.

(End)