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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)