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A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 20, 330, 1224, 2726, 4807, 7458, 10679, 14470, 18831, 23762, 29263, 35334, 41975, 49186, 56967, 65318, 74239, 83730, 93791, 104422, 115623, 127394, 139735, 152646, 166127, 180178, 194799, 209990, 225751, 242082, 258983, 276454, 294495 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 7 of A187507.

LINKS

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

FORMULA

Empirical: a(n) = 285*n^2 - 1624*n + 2210 for n>5.

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

G.f.: x^3*(1 + x)*(20 + 250*x + 44*x^2 - 20*x^3 - 9*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

EXAMPLE

Some solutions for 4 X 4:

..0..0..0..0....1..2..0..0....0..5..3..1....0..0..1..2....4..5..6..0

..0..7..0..0....0..3..4..0....0..6..4..2....0..7..5..3....2..3..7..0

..1..5..6..0....0..7..5..0....0..7..0..0....0..0..6..4....0..1..0..0

..2..3..4..0....0..0..6..0....0..0..0..0....0..0..0..0....0..0..0..0

CROSSREFS

Cf. A187507.

Sequence in context: A078230 A304723 A273590 * A144507 A084032 A166984

Adjacent sequences:  A187509 A187510 A187511 * A187513 A187514 A187515

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 10 2011

STATUS

approved

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Last modified October 16 12:23 EDT 2021. Contains 348041 sequences. (Running on oeis4.)