A188155 Number of 10-step self-avoiding walks on an n X n square summed over all starting positions.

0, 0, 0, 3696, 26000, 82032, 175312, 303328, 464304, 657848, 883928, 1142544, 1433696, 1757384, 2113608, 2502368, 2923664, 3377496, 3863864, 4382768, 4934208, 5518184, 6134696, 6783744, 7465328, 8179448, 8926104, 9705296, 10517024

Offset

1,4

Comments

Row 10 of A188147.

Links

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

Formula

Empirical: a(n) = 16268*n^2 - 115548*n + 186528 for n>8.

Conjectures from Colin Barker, Apr 27 2018: (Start)

G.f.: 8*x^4*(462 + 1864*x + 1890*x^2 + 440*x^3 - 314*x^4 - 222*x^5 - 49*x^6 - 4*x^7) / (1 - x)^3.

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

(End)

Example

Some solutions for 4 X 4:
..0..8..9.10....0..7..8..9....0..3..4..5....0..0..6..7....1..0..0.10
..0..7..6..1....0..6..5.10....1..2..7..6....0..4..5..8....2..7..8..9
..0..0..5..2....0..3..4..0...10..9..8..0....0..3..2..9....3..6..0..0
..0..0..4..3....0..2..1..0....0..0..0..0....0..0..1.10....4..5..0..0

Crossrefs

Cf. A188147.

Sequence in context: A234486 A097500 A186198 * A061660 A219067 A035780

Adjacent sequences: A188152 A188153 A188154 * A188156 A188157 A188158

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved