A187381 Number of 7-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

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

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