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A187514 Number of 9-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 6, 450, 2872, 8522, 17564, 29834, 45255, 63814, 85511, 110346, 138319, 169430, 203679, 241066, 281591, 325254, 372055, 421994, 475071, 531286, 590639, 653130, 718759, 787526, 859431, 934474, 1012655, 1093974, 1178431, 1266026, 1356759 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 9 of A187507.

LINKS

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

FORMULA

Empirical: a(n) = 1569*n^2 - 11252*n + 19434 for n>7.

Conjectures from Colin Barker, Apr 24 2018: (Start)

G.f.: x^3*(6 + 432*x + 1540*x^2 + 1250*x^3 + 164*x^4 - 164*x^5 - 77*x^6 - 13*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 4 X 4:

..5..6..7..0....5..3..0..0....0..0..0..0....0..0..0..0....1..2..3..0

..3..4..8..9....6..4..2..0....7..8..9..1....3..4..5..6....0..0..4..5

..0..2..0..0....7..8..0..1....0..6..4..2....0..2..9..7....0..0..8..6

..0..0..1..0....0..9..0..0....0..0..5..3....0..0..1..8....0..0..9..7

CROSSREFS

Cf. A187507.

Sequence in context: A001328 A174777 A265168 * A258873 A244195 A338943

Adjacent sequences:  A187511 A187512 A187513 * A187515 A187516 A187517

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 10 2011

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)