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A187170 Number of 9-step self-avoiding walks on a n X n X n cube summed over all starting positions. 2
0, 0, 167016, 2013360, 8227752, 21274896, 43422072, 76964016, 124223214, 187527168, 269203674, 371580528, 496985526, 647746464, 826191138, 1034647344, 1275442878, 1550905536, 1863363114, 2215143408, 2608574214, 3045983328 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 9 of A187162.

LINKS

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

FORMULA

Empirical: a(n) = 387966*n^3 - 2452704*n^2 + 4766544*n - 2833872 for n>7.

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

G.f.: 6*x^3*(27836 + 224216*x + 196068*x^2 - 37336*x^3 - 32904*x^4 + 4576*x^5 + 4625*x^6 + 836*x^7 + 49*x^8) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>11.

(End)

CROSSREFS

Cf. A187162.

Sequence in context: A250931 A319295 A235846 * A047829 A236494 A236489

Adjacent sequences:  A187167 A187168 A187169 * A187171 A187172 A187173

KEYWORD

nonn,walk

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified January 25 23:08 EST 2020. Contains 331270 sequences. (Running on oeis4.)