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

1,3

Comments

Row 5 of A188777

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)

Example

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

Crossrefs

Sequence in context: A325292 A326552 A303933 * A015023 A225168 A332158

Adjacent sequences: A188777 A188778 A188779 * A188781 A188782 A188783

Keyword

nonn

Author

R. H. Hardin Apr 10 2011

Status

approved