A187592 Number of 9-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 13, 2792, 27252, 103108, 246792, 458018, 732810, 1069534, 1468190, 1928778, 2451298, 3035750, 3682134, 4390450, 5160698, 5992878, 6886990, 7843034, 8861010, 9940918, 11082758, 12286530, 13552234, 14879870, 16269438, 17720938, 19234370

Offset

1,3

Comments

Row 9 of A187586.

Links

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

Formula

Empirical: a(n) = 30966*n^2 - 251630*n + 489234 for n>7.

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

G.f.: x^3*(13 + 2753*x + 18915*x^2 + 29715*x^3 + 16432*x^4 - 286*x^5 - 3976*x^6 - 1634*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

Example

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

Crossrefs

Cf. A187586.

Sequence in context: A348817 A195537 A203692 * A287036 A208315 A296174

Adjacent sequences: A187589 A187590 A187591 * A187593 A187594 A187595

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved