A188783 Number of 8-turn bishop's tours on an n X n board summed over all starting positions

0, 0, 0, 384, 88264, 1665344, 14497784, 80088992, 335122320, 1142391712, 3358831216, 8772323808, 20882774744, 46000760736, 95075730152, 186010966464, 347367851808, 622687135680, 1077266143968, 1805545001664, 2942598571752

Offset

1,4

Comments

Row 8 of A188777

Links

Table of n, a(n) for n=1..21.

Formula

From Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: Recurrence: a(n) = a(n-17) - 5*a(n-16) + 4*a(n-15) + 20*a(n-14) - 40*a(n-13) - 16*a(n-12) + 100*a(n-11) - 44*a(n-10) - 110*a(n-9) + 110*a(n-8) + 44*a(n-7) - 100*a(n-6) + 16*a(n-5) + 40*a(n-4) - 20*a(n-3) - 4*a(n-2) + 5*a(n-1)

Empirical: G.f.: 8*x^4*(48 + 10841*x + 164036*x^2 + 980511*x^3 + 2981932*x^4 + 5786766*x^5 + 6924788*x^6 + 5849090*x^7 + 3007252*x^8 + 1111577*x^9 + 201048*x^10 + 23391*x^11)/((1-x)^10*(1+x)^6)

Empirical: a(n) = -31395/16 + 31519*n/2 - 50452903*n^2/1260 + 13521503*n^3/270 - 4517641*n^4/120 + 224087*n^5/12 - 93658*n^6/15 + 60857*n^7/45 - 428119*n^8/2520 + 503*n^9/54 + (-1)^n*(31395/16 - 55203*n/10 + 20473*n^2/4 - 4275*n^3/2 + 3349*n^4/8 - 629*n^5/20)

(End)

Example

Some solutions for 4X4
..0..3..0..8....4..0..7..0....4..0..8..0....0..5..0..1....0..8..0..1
..6..0..2..0....0..6..0..1....0..2..0..7....6..0..3..0....5..0..3..0
..0..7..0..4....8..0..3..0....1..0..5..0....0..8..0..4....0..4..0..7
..1..0..5..0....0..2..0..5....0..6..0..3....2..0..7..0....2..0..6..0

Crossrefs

Sequence in context: A190401 A256727 A023098 * A008692 A364181 A193313

Adjacent sequences: A188780 A188781 A188782 * A188784 A188785 A188786

Keyword

nonn

Author

R. H. Hardin Apr 10 2011

Status

approved