A187161 Number of 8-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 0, 472, 3504, 10576, 23340, 40448, 61900, 87696, 117836, 152320, 191148, 234320, 281836, 333696, 389900, 450448, 515340, 584576, 658156, 736080, 818348, 904960, 995916, 1091216, 1190860, 1294848, 1403180, 1515856, 1632876, 1754240

Offset

1,5

Comments

Row 8 of A187155.

Links

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

Formula

Empirical: a(n) = 2172*n^2 - 19816*n + 42860 for n>6.

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

G.f.: 4*x^5*(118 + 522*x + 370*x^2 + 413*x^3 - 337*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

Example

Some solutions for 5 X 5:
..0..0..3..0..0....0..0..7..0..0....0..0..0..0..0....0..2..0..0..0
..0..2..0..4..0....0..6..0..8..0....0..0..7..0..0....3..0..1..0..0
..1..0..7..0..5....0..0..5..0..0....0..8..0..6..0....0..4..0..0..0
..0..8..0..6..0....0..4..0..2..0....1..0..3..0..5....5..0..7..0..0
..0..0..0..0..0....0..0..3..0..1....0..2..0..4..0....0..6..0..8..0

Crossrefs

Cf. A187155.

Sequence in context: A260102 A260135 A259640 * A249534 A180838 A006180

Adjacent sequences: A187158 A187159 A187160 * A187162 A187163 A187164

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved