A188786 Number of 3-step self-avoiding walks on an n X n X n X n 4-cube summed over all starting positions.

0, 192, 1944, 7936, 22200, 50112, 98392, 175104, 289656, 452800, 676632, 974592, 1361464, 1853376, 2467800, 3223552, 4140792, 5241024, 6547096, 8083200, 9874872, 11948992, 14333784, 17058816, 20155000, 23654592, 27591192, 31999744, 36916536

Offset

1,2

Comments

Row 3 of A188784.

Links

R. H. Hardin, Table of n, a(n) for n = 1..43

Formula

Empirical: a(n) = 56*n^4 - 112*n^3 + 48*n^2 for n>1.

Conjectures from Colin Barker, Apr 28 2018: (Start)

G.f.: 8*x^2*(24 + 123*x + 17*x^2 + 5*x^3 - x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.

(End)

Crossrefs

Cf. A188784.

Sequence in context: A183685 A254846 A051526 * A362510 A251442 A251435

Adjacent sequences: A188783 A188784 A188785 * A188787 A188788 A188789

Keyword

nonn

Author

R. H. Hardin, Apr 10 2011

Status

approved