A187159 Number of 6-step one space at a time bishop's tours on an n X n board summed over all starting positions.

0, 0, 0, 56, 456, 1588, 3288, 5556, 8392, 11796, 15768, 20308, 25416, 31092, 37336, 44148, 51528, 59476, 67992, 77076, 86728, 96948, 107736, 119092, 131016, 143508, 156568, 170196, 184392, 199156, 214488, 230388, 246856, 263892, 281496, 299668

Offset

1,4

Comments

Row 6 of A187155.

Links

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

Formula

Empirical: a(n) = 284*n^2 - 1992*n + 3316 for n>4.

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

G.f.: 4*x^4*(14 + 72*x + 97*x^2 - 41*x^3) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(End)

Example

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

Crossrefs

Cf. A187155.

Sequence in context: A287702 A008447 A076647 * A220048 A257707 A067234

Adjacent sequences: A187156 A187157 A187158 * A187160 A187161 A187162

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved