A187853 Number of 5-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

0, 0, 5328, 49776, 177040, 408048, 744696, 1183632, 1723120, 2362864, 3102864, 3943120, 4883632, 5924400, 7065424, 8306704, 9648240, 11090032, 12632080, 14274384, 16016944, 17859760, 19802832, 21846160, 23989744, 26233584, 28577680

Offset

1,3

Comments

Row 5 of A187850.

Links

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

Formula

Empirical: a(n) = 50128*n^2 - 312688*n + 476944 for n>7.

Conjectures from Colin Barker, Apr 26 2018: (Start)

G.f.: 8*x^3*(666 + 4224*x + 5462*x^2 + 2616*x^3 + 237*x^4 - 419*x^5 - 217*x^6 - 37*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

Example

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

Crossrefs

Cf. A187850.

Sequence in context: A133152 A252199 A317917 * A236274 A278895 A317918

Adjacent sequences: A187850 A187851 A187852 * A187854 A187855 A187856

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved