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

1,3

Comments

Row 5 of A187046.

Links

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

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)

Example

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

Crossrefs

Cf. A187046.

Sequence in context: A042525 A028449 A209840 * A367707 A221157 A015006

Adjacent sequences: A187046 A187047 A187048 * A187050 A187051 A187052

Keyword

nonn

Author

R. H. Hardin, Mar 02 2011

Status

approved