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A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 12, 390, 1910, 4880, 9250, 14969, 22026, 30421, 40154, 51225, 63634, 77381, 92466, 108889, 126650, 145749, 166186, 187961, 211074, 235525, 261314, 288441, 316906, 346709, 377850, 410329, 444146, 479301, 515794, 553625, 592794, 633301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 8 of A187507.

LINKS

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

FORMULA

Empirical: a(n) = 669*n^2 - 4316*n + 6681 for n>6.

Empirical g.f.: x^3*(12 + 354*x + 776*x^2 + 308*x^3 - 50*x^4 - 51*x^5 - 11*x^6) / (1 - x)^3. - Colin Barker, Nov 27 2017

EXAMPLE

Some solutions for 4X4

..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0

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

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

..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....0..0..0..0

CROSSREFS

Sequence in context: A196459 A193132 A326214 * A138914 A326220 A308129

Adjacent sequences:  A187510 A187511 A187512 * A187514 A187515 A187516

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 10 2011

STATUS

approved

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Last modified September 20 19:41 EDT 2021. Contains 347589 sequences. (Running on oeis4.)