A187160 Number of 7-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 16, 544, 2328, 6172, 11576, 18540, 27064, 37148, 48792, 61996, 76760, 93084, 110968, 130412, 151416, 173980, 198104, 223788, 251032, 279836, 310200, 342124, 375608, 410652, 447256, 485420, 525144, 566428, 609272, 653676, 699640, 747164

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 7 of A187155.

Examples

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

Links

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

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 780*n^2 - 6296*n + 12024 for n>5.

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

G.f.: 4*x^4*(4 + 124*x + 186*x^2 + 201*x^3 - 125*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)