A187587 Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions

0, 5, 84, 286, 604, 1038, 1588, 2254, 3036, 3934, 4948, 6078, 7324, 8686, 10164, 11758, 13468, 15294, 17236, 19294, 21468, 23758, 26164, 28686, 31324, 34078, 36948, 39934, 43036, 46254, 49588, 53038, 56604, 60286, 64084, 67998, 72028, 76174, 80436, 84814

Offset

1,2

Comments

Row 4 of A187586

Links

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

Formula

Empirical: a(n) = 58*n^2 - 204*n + 174 for n>2.

Empirical G.f.: x^2*(5+69*x+49*x^2-7*x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

Example

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

Crossrefs

Sequence in context: A111834 A271219 A359110 * A006471 A258391 A061628

Adjacent sequences: A187584 A187585 A187586 * A187588 A187589 A187590

Keyword

nonn

Author

R. H. Hardin Mar 11 2011

Status

approved