A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

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

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