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A188154 Number of 9-step self-avoiding walks on an n X n square summed over all starting positions. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)