A188779 Number of 4-turn bishop's tours on an n X n board summed over all starting positions

0, 0, 24, 328, 1720, 5816, 15424, 34736, 69776, 128528, 221448, 361528, 564872, 850696, 1241968, 1765344, 2451872, 3336864, 4460664, 5868456, 7611096, 9744856, 12332320, 15442064, 19149616, 23537072, 28694120, 34717592, 41712552, 49791784

Offset

1,3

Comments

Row 4 of A188777

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

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

Empirical: G.f.: 8*x^3*(3 + 29*x + 63*x^2 + 43*x^3 + 14*x^4)/((1-x)^6*(1+x)^2)

Empirical: a(n) = -2 + 257*n/15 - 109*n^2/3 + 106*n^3/3 - 47*n^4/3 + 38*n^5/15 + (-1)^n*(2-n)

(End)

Example

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

Crossrefs

Sequence in context: A004317 A295250 A295649 * A262291 A267838 A045543

Adjacent sequences: A188776 A188777 A188778 * A188780 A188781 A188782

Keyword

nonn

Author

R. H. Hardin Apr 10 2011

Status

approved