A187165 Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 96, 1104, 3984, 9612, 18888, 32712, 51984, 77604, 110472, 151488, 201552, 261564, 332424, 415032, 510288, 619092, 742344, 880944, 1035792, 1207788, 1397832, 1606824, 1835664, 2085252, 2356488, 2650272, 2967504, 3309084, 3675912, 4068888

Offset

1,2

Comments

Row 4 of A187162.

Links

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

Formula

Empirical: a(n) = 150*n^3 - 426*n^2 + 312*n - 48 for n>2.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 12*x^2*(8 + 60*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - x)^4.

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

(End)

Example

A solution for 2 X 2 X 2:
..2..0.....3..4
..1..0.....0..0

Crossrefs

Cf. A187162.

Sequence in context: A027628 A182684 A232918 * A229533 A282017 A263567

Adjacent sequences: A187162 A187163 A187164 * A187166 A187167 A187168

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved