A187168 Number of 7-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 192, 25344, 177120, 568248, 1298016, 2466510, 4175136, 6525450, 9619008, 13557366, 18442080, 24374706, 31456800, 39789918, 49475616, 60615450, 73310976, 87663750, 103775328, 121747266, 141681120, 163678446, 187840800, 214269738

Offset

1,2

Comments

Row 7 of A187162.

Links

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

Formula

Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.

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

G.f.: 6*x^2*(32 + 4096*x + 12816*x^2 + 1844*x^3 - 2240*x^4 + 133*x^5 + 220*x^6 + 25*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.

(End)

Example

A solution for 3 X 3 X 3:
..0..0..0.....0..0..0.....0..0..0
..0..0..0.....1..2..0.....0..0..0
..7..0..0.....6..3..0.....5..4..0

Crossrefs

Cf. A187162.

Sequence in context: A199007 A199006 A001290 * A078272 A299993 A208444

Adjacent sequences: A187165 A187166 A187167 * A187169 A187170 A187171

Keyword

nonn,walk

Author

R. H. Hardin, Mar 06 2011

Status

approved