A187049 Number of 5-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 8, 456, 2896, 9216, 20648, 37472, 59524, 86656, 118868, 156160, 198532, 245984, 298516, 356128, 418820, 486592, 559444, 637376, 720388, 808480, 901652, 999904, 1103236, 1211648, 1325140, 1443712, 1567364, 1696096, 1829908, 1968800, 2112772

Offset: 1

Author

R. H. Hardin, Mar 02 2011

Keywords

• nonn

Comments

Row 5 of A187046.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..35

Crossrefs

Cf. A187046.

Formula

Empirical: a(n) = 2540*n^2 - 21128*n + 43936 for n>7.

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

G.f.: 4*x^3*(2 + 108*x + 388*x^2 + 472*x^3 + 308*x^4 + 70*x^5 - 41*x^6 - 37*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)