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

1,3

Comments

Row 9 of A188147.

Links

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

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)

Example

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

Crossrefs

Cf. A188147.

Sequence in context: A263553 A049215 A221658 * A268151 A269824 A178721

Adjacent sequences: A188151 A188152 A188153 * A188155 A188156 A188157

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved