A187161 Number of 8-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 0, 472, 3504, 10576, 23340, 40448, 61900, 87696, 117836, 152320, 191148, 234320, 281836, 333696, 389900, 450448, 515340, 584576, 658156, 736080, 818348, 904960, 995916, 1091216, 1190860, 1294848, 1403180, 1515856, 1632876, 1754240

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 8 of A187155.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 2172*n^2 - 19816*n + 42860 for n>6.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 4*x^5*(118 + 522*x + 370*x^2 + 413*x^3 - 337*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)