A187378 Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions

0, 4, 40, 132, 278, 478, 732, 1040, 1402, 1818, 2288, 2812, 3390, 4022, 4708, 5448, 6242, 7090, 7992, 8948, 9958, 11022, 12140, 13312, 14538, 15818, 17152, 18540, 19982, 21478, 23028, 24632, 26290, 28002, 29768, 31588, 33462, 35390, 37372, 39408

Offset

1,2

Comments

Row 4 of A187377

Links

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

Formula

Empirical: a(n) = 27*n^2 - 97*n + 88 for n>2.

Empirical G.f.: 2*x^2*(2+14*x+12*x^2-x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

Example

Some solutions for 4X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..2....4..0..0..0
..3..0..0..0....0..0..2..0....0..0..0..0....0..0..1..3....0..3..0..0
..4..2..0..0....0..0..3..1....3..1..0..0....0..0..0..4....0..0..2..0
..0..0..1..0....0..0..4..0....4..2..0..0....0..0..0..0....0..0..0..1

Crossrefs

Sequence in context: A069539 A063997 A355841 * A199833 A248964 A224086

Adjacent sequences: A187375 A187376 A187377 * A187379 A187380 A187381

Keyword

nonn

Author

R. H. Hardin Mar 09 2011

Status

approved