A188154 Number of 9-step self-avoiding walks on an n X n square summed over all starting positions.

0, 0, 40, 2640, 14520, 39792, 78168, 128688, 191068, 265280, 351324, 449200, 558908, 680448, 813820, 959024, 1116060, 1284928, 1465628, 1658160, 1862524, 2078720, 2306748, 2546608, 2798300, 3061824, 3337180, 3624368, 3923388, 4234240, 4556924

Offset: 1

Author

R. H. Hardin, Mar 22 2011

Keywords

• nonn

Comments

Row 9 of A188147.

Examples

			Some solutions for 3 X 3:
..3..4..5....1..2..3....3..4..5....9..2..1....3..4..5....9..4..3....7..6..5
..2..7..6....8..7..4....2..9..6....8..3..4....2..1..6....8..5..2....8..3..4
..1..8..9....9..6..5....1..8..7....7..6..5....9..8..7....7..6..1....9..2..1
		

Links

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

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 5916*n^2 - 38192*n + 55600 for n>7.

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

G.f.: 4*x^3*(10 + 630*x + 1680*x^2 + 1028*x^3 - 72*x^4 - 240*x^5 - 71*x^6 - 7*x^7) / (1 - x)^3.

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

(End)