A187157 Number of 4-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 8, 92, 248, 476, 776, 1148, 1592, 2108, 2696, 3356, 4088, 4892, 5768, 6716, 7736, 8828, 9992, 11228, 12536, 13916, 15368, 16892, 18488, 20156, 21896, 23708, 25592, 27548, 29576, 31676, 33848, 36092, 38408, 40796, 43256, 45788, 48392, 51068, 53816

Offset

1,3

Comments

Row 4 of A187155.

Links

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

Formula

Empirical: a(n) = 36*n^2 - 168*n + 188 for n>2.

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

G.f.: 4*x^3*(2 + 17*x - x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

(End)

Example

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

Crossrefs

Cf. A187155.

Sequence in context: A302614 A220573 A303743 * A332597 A331448 A215057

Adjacent sequences: A187154 A187155 A187156 * A187158 A187159 A187160

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved