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

1,2

Comments

Row 8 of A187162.

Links

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

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)

Example

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

Crossrefs

Cf. A187162.

Sequence in context: A028473 A130118 A288909 * A187464 A221735 A272462

Adjacent sequences: A187166 A187167 A187168 * A187170 A187171 A187172

Keyword

nonn,walk

Author

R. H. Hardin, Mar 06 2011

Status

approved