A188782 Number of 7-turn bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 784, 40496, 451104, 2803552, 12139552, 41792672, 121269248, 310362944, 718151344, 1534460624, 3067048224, 5801302304, 10464095808, 18125622336, 30299632896, 49104515712, 77410664016, 119081302128, 179178580768

Offset

1,4

Comments

Row 7 of A188777.

Links

R. H. Hardin, Table of n, a(n) for n = 1..28

Formula

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

Empirical: Recurrence: a(n) = a(n-14) - 4*a(n-13) + a(n-12) + 16*a(n-11) - 19*a(n-10) - 20*a(n-9) + 45*a(n-8) - 45*a(n-6) + 20*a(n-5) + 19*a(n-4) - 16*a(n-3) - a(n-2) + 4*a(n-1).

Empirical: G.f.: 16*x^4*(49 + 2335*x + 18119*x^2 + 65761*x^3 + 125593*x^4 + 154411*x^5 + 109333*x^6 + 52763*x^7 + 12090*x^8 + 1722*x^9)/((1-x)^9*(1+x)^5).

Empirical: a(n) = 6421/16 - 581677*n/210 + 2022619*n^2/315 - 340262*n^3/45 + 1915471*n^4/360 - 106466*n^5/45 + 29363*n^6/45 - 31916*n^7/315 + 16943*n^8/2520 + (-1)^n*(-6421/16 + 1645*n/2 - 557*n^2 + 155*n^3 - 123*n^4/8).

(End)

Example

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

Crossrefs

Cf. A188777.

Sequence in context: A203790 A223493 A231976 * A184601 A151658 A231771

Adjacent sequences: A188779 A188780 A188781 * A188783 A188784 A188785

Keyword

nonn

Author

R. H. Hardin, Apr 10 2011

Status

approved