A188780 Number of 5-turn bishop's tours on an n X n board summed over all starting positions.

0, 0, 8, 584, 5464, 26360, 91120, 252720, 603696, 1288592, 2525400, 4620728, 7998984, 13219528, 21014336, 32306400, 48256608, 70282656, 100115880, 139819944, 191858360, 259112216, 344959120, 453289232, 588596368, 755991600

Offset: 1

Author

R. H. Hardin Apr 10 2011

Keywords

• nonn

Comments

Row 5 of A188777

Examples

			Some solutions for 4X4
..0..5..0..0....0..5..0..0....0..5..0..0....0..0..2..0....0..4..0..0
..1..0..4..0....0..0..1..0....0..0..3..0....0..5..0..3....0..0..3..0
..0..3..0..0....0..2..0..4....0..2..0..4....1..0..4..0....0..2..0..5
..0..0..2..0....0..0..3..0....1..0..0..0....0..0..0..0....0..0..1..0
		

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) -8*a(n-3) +14*a(n-4) -14*a(n-6) +8*a(n-7) +3*a(n-8) -4*a(n-9) +a(n-10)

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

Empirical: G.f.: 8*x^3*(1 + 69*x + 394*x^2 + 790*x^3 + 829*x^4 + 357*x^5 + 84*x^6)/((1-x)^7*(1+x)^3)

Empirical: a(n) = 51/4 - 913*n/10 + 69203*n^2/360 - 602*n^3/3 + 1007*n^4/9 - 473*n^5/15 + 631*n^6/180 + (-1)^n*(-51/4 + 25*n/2 - 23*n^2/8)

(End)