A187051 Number of 7-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, 400, 14024, 86608, 285048, 668176, 1272720, 2110944, 3180724, 4475176, 5989600, 7722744, 9674608, 11845192, 14234496, 16842520, 19669264, 22714728, 25978912, 29461816, 33163440, 37083784, 41222848, 45580632, 50157136, 54952360

Offset

1,4

Comments

Row 7 of A187046.

Links

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

Formula

Empirical: a(n) = 109360*n^2 - 1219576*n + 3362248 for n>11.

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

G.f.: 4*x^4*(100 + 3206*x + 11434*x^2 + 16724*x^3 + 14708*x^4 + 9182*x^5 + 3066*x^6 - 531*x^7 - 1721*x^8 - 1175*x^9 - 313*x^10) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

(End)

Example

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

Crossrefs

Cf. A187046.

Sequence in context: A192076 A006764 A108034 * A231288 A210262 A151608

Adjacent sequences: A187048 A187049 A187050 * A187052 A187053 A187054

Keyword

nonn

Author

R. H. Hardin, Mar 02 2011

Status

approved