A188778 Number of 3-turn bishop's tours on an n X n board summed over all starting positions

0, 0, 28, 152, 488, 1192, 2468, 4560, 7760, 12400, 18860, 27560, 38968, 53592, 71988, 94752, 122528, 156000, 195900, 243000, 298120, 362120, 435908, 520432, 616688, 725712, 848588, 986440, 1140440, 1311800, 1501780, 1711680, 1942848, 2196672

Offset

1,3

Comments

Row 3 of A188777

Links

R. H. Hardin, Table of n, a(n) for n = 1..42

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6)

Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 4*x^3*(7 + 10*x + 5*x^2)/((1-x)^5*(1+x))

Empirical: a(n) = 1/4 - 10*n/3 + 23*n^2/3 - 20*n^3/3 + 11*n^4/6 - (-1)^n/4

(End)

Example

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

Crossrefs

Sequence in context: A028380 A219887 A271636 * A002593 A015881 A026910

Adjacent sequences: A188775 A188776 A188777 * A188779 A188780 A188781

Keyword

nonn

Author

R. H. Hardin Apr 10 2011

Status

approved