A187380 Number of 6-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 24, 264, 832, 1810, 3154, 4864, 6940, 9382, 12190, 15364, 18904, 22810, 27082, 31720, 36724, 42094, 47830, 53932, 60400, 67234, 74434, 82000, 89932, 98230, 106894, 115924, 125320, 135082, 145210, 155704, 166564, 177790, 189382, 201340

Offset

1,3

Links

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

Formula

Empirical: a(n) = 183*n^2 - 1035*n + 1432 for n>4.

Conjectures from Colin Barker, Apr 24 2018: (Start)

G.f.: 2*x^3*(12 + 96*x + 56*x^2 + 41*x^3 - 22*x^4) / (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..6..4..0....4..0..0..0....0..1..0..0....0..5..0..0....0..1..0..0
..1..3..5..0....5..3..0..0....0..2..0..0....4..6..0..0....0..2..0..6
..2..0..0..0....6..0..2..0....0..3..5..0....1..3..0..0....0..3..5..0
..0..0..0..0....0..0..0..1....0..4..6..0....2..0..0..0....0..4..0..0

Crossrefs

Row 6 of A187377.

Sequence in context: A009175 A308054 A296916 * A000145 A286346 A126904

Adjacent sequences: A187377 A187378 A187379 * A187381 A187382 A187383

Keyword

nonn

Author

R. H. Hardin, Mar 09 2011

Status

approved