A187158 Number of 5-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 72, 388, 904, 1620, 2536, 3652, 4968, 6484, 8200, 10116, 12232, 14548, 17064, 19780, 22696, 25812, 29128, 32644, 36360, 40276, 44392, 48708, 53224, 57940, 62856, 67972, 73288, 78804, 84520, 90436, 96552, 102868, 109384, 116100, 123016, 130132

Offset

1,4

Comments

Row 5 of A187155.

Links

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

Formula

Empirical: a(n) = 100*n^2 - 584*n + 808 for n>3.

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

G.f.: 4*x^4*(18 + 43*x - 11*x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

Example

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

Crossrefs

Cf. A187155.

Sequence in context: A303621 A084479 A084478 * A164377 A156632 A353218

Adjacent sequences: A187155 A187156 A187157 * A187159 A187160 A187161

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved