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

1,4

Comments

Row 7 of A187155.

Links

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

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)

Example

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

Crossrefs

Cf. A187155.

Sequence in context: A196298 A361310 A274136 * A196216 A196683 A131515

Adjacent sequences: A187157 A187158 A187159 * A187161 A187162 A187163

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved