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A188155 Number of 10-step self-avoiding walks on an n X n square summed over all starting positions. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)