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A187169 Number of 8-step self-avoiding walks on a n X n X n cube summed over all starting positions. 2
0, 144, 67824, 608928, 2188608, 5299056, 10416624, 18026640, 28617228, 42676728, 60693480, 83155824, 110552100, 143370648, 182099808, 227227920, 279243324, 338634360, 405889368, 481496688, 565944660, 659721624, 763315920, 877215888 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)