A187050 Number of 6-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 584, 6952, 29500, 79088, 162320, 281320, 435436, 623508, 845084, 1100164, 1388748, 1710836, 2066428, 2455524, 2878124, 3334228, 3823836, 4346948, 4903564, 5493684, 6117308, 6774436, 7465068, 8189204, 8946844, 9737988, 10562636

Offset

1,4

Comments

Row 6 of A187046.

Links

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

Formula

Empirical: a(n) = 16752*n^2 - 163720*n + 397436 for n>9.

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

G.f.: 4*x^3*(146 + 1300*x + 2599*x^2 + 2715*x^3 + 1651*x^4 + 531*x^5 - 163*x^6 - 290*x^7 - 113*x^8) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)

Example

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

Crossrefs

Cf. A187046.

Sequence in context: A236491 A235433 A205069 * A252195 A037995 A250627

Adjacent sequences: A187047 A187048 A187049 * A187051 A187052 A187053

Keyword

nonn

Author

R. H. Hardin, Mar 02 2011

Status

approved