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

Author

R. H. Hardin, Mar 22 2011

Keywords

• nonn

Comments

Row 10 of A188147.

Examples

			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
		

Links

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

Crossrefs

Cf. A188147.

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)