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A187381 Number of 7-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 18, 324, 1418, 3448, 6581, 10688, 15769, 21824, 28853, 36856, 45833, 55784, 66709, 78608, 91481, 105328, 120149, 135944, 152713, 170456, 189173, 208864, 229529, 251168, 273781, 297368, 321929, 347464, 373973, 401456, 429913, 459344 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 7 of A187377.

LINKS

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

FORMULA

Empirical: a(n) = 487*n^2 - 3198*n + 5104 for n>5.

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

G.f.: x^3*(18 + 270*x + 500*x^2 + 148*x^3 + 167*x^4 - 129*x^5) / (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..6....0..0..0..0....0..0..7..0....0..5..3..1....0..0..2..0

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

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

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

CROSSREFS

Cf. A187377.

Sequence in context: A207783 A207022 A207366 * A207109 A207465 A207240

Adjacent sequences:  A187378 A187379 A187380 * A187382 A187383 A187384

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 09 2011

STATUS

approved

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Last modified August 19 16:39 EDT 2022. Contains 356229 sequences. (Running on oeis4.)