A187170 Number of 9-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 0, 167016, 2013360, 8227752, 21274896, 43422072, 76964016, 124223214, 187527168, 269203674, 371580528, 496985526, 647746464, 826191138, 1034647344, 1275442878, 1550905536, 1863363114, 2215143408, 2608574214, 3045983328

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