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

Author

R. H. Hardin, Apr 10 2011

Keywords

• nonn

Comments

Row 6 of A188777.

Examples

			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
		

Links

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

Crossrefs

Cf. A188777.

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)