A188781 Number of 6-turn bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 840, 15824, 112680, 516160, 1778608, 5082912, 12622640, 28225472, 58013112, 111476080, 202472856, 350897664, 584067552, 939135552, 1464903648, 2225144448, 3300867240, 4794722064, 6833735304, 9574980800, 13208790672

Offset

1,4

Comments

Row 6 of A188777.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) -12*a(n-3) +17*a(n-4) +8*a(n-5) -28*a(n-6) +8*a(n-7) +17*a(n-8) -12*a(n-9) -2*a(n-10) +4*a(n-11) -a(n-12).

From Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 8*x^4*(105 + 1558*x + 6383*x^2 + 13396*x^3 + 14367*x^4 + 9654*x^5 + 2937*x^6 + 528*x^7)/((1-x)^8*(1+x)^4).

Empirical: a(n) = -297/4 + 13961*n/28 - 32551*n^2/30 + 54158*n^3/45 - 4625*n^4/6 + 5189*n^5/18 - 872*n^6/15 + 1529*n^7/315 + (-1)^n*(297/4 - 439*n/4 + 99*n^2/2 - 7*n^3).

(End)

Example

Some solutions for 4 X 4
..0..0..4..0....0..2..0..6....0..4..0..1....0..3..0..0....0..5..0..3
..0..3..0..1....1..0..4..0....5..0..2..0....2..0..4..0....6..0..4..0
..5..0..2..0....0..5..0..3....0..0..0..3....0..1..0..5....0..2..0..0
..0..6..0..0....0..0..0..0....0..0..6..0....0..0..6..0....1..0..0..0

Crossrefs

Cf. A188777.

Sequence in context: A215230 A171260 A166758 * A166764 A226268 A218410

Adjacent sequences: A188778 A188779 A188780 * A188782 A188783 A188784

Keyword

nonn

Author

R. H. Hardin, Apr 10 2011

Status

approved