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

Author

R. H. Hardin, Apr 10 2011

Keywords

• nonn

Comments

Row 7 of A188777.

Examples

			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
		

Links

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

Crossrefs

Cf. A188777.

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)