A187515 Number of 10-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 0, 398, 3868, 13796, 31548, 56952, 89684, 129637, 176796, 231161, 292732, 361509, 437492, 520681, 611076, 708677, 813484, 925497, 1044716, 1171141, 1304772, 1445609, 1593652, 1748901, 1911356, 2081017, 2257884, 2441957, 2633236

Offset

1,4

Comments

Row 10 of A187507.

Links

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

Formula

Empirical: a(n) = 3603*n^2 - 28504*n + 54377 for n>8.

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

G.f.: x^4*(398 + 2674*x + 3386*x^2 + 1366*x^3 - 172*x^4 - 324*x^5 - 107*x^6 - 15*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)

Example

Some solutions for 4 X 4:
..1..0..0..0....7..8..9.10....0..7..8..9....0..5..0..1....0..0..0..1
..2..3..4..5....0..6..0..0....4..5..6.10....8..6..4..2....0..0..0..2
..0.10..8..6....0..4..5..0....0..3..1..0....9..7..0..3....9..7..5..3
..0..0..9..7....1..2..3..0....0..0..2..0...10..0..0..0...10..8..6..4

Crossrefs

Cf. A187507.

Sequence in context: A158316 A236713 A235958 * A235569 A261768 A274446

Adjacent sequences: A187512 A187513 A187514 * A187516 A187517 A187518

Keyword

nonn

Author

R. H. Hardin, Mar 10 2011

Status

approved