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A186864 Number of 5-step king's tours on an n X n board summed over all starting positions. 1
0, 0, 1208, 6712, 17280, 32520, 52432, 77016, 106272, 140200, 178800, 222072, 270016, 322632, 379920, 441880, 508512, 579816, 655792, 736440, 821760, 911752, 1006416, 1105752, 1209760, 1318440, 1431792, 1549816, 1672512, 1799880, 1931920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 5 of A186861.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..32

FORMULA

Empirical: a(n) = 2336*n^2 - 10456*n + 11160 for n>3.

Conjectures from Colin Barker, Apr 19 2018: (Start)

G.f.: 8*x^3*(151 + 386*x + 96*x^2 - 49*x^3) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

EXAMPLE

Some solutions for 3 X 3:

..0..5..0....0..1..2....3..1..0....3..2..1....0..1..2....0..1..2....0..5..0

..2..3..4....0..3..5....2..4..0....5..4..0....0..4..3....0..5..3....1..3..4

..1..0..0....0..4..0....5..0..0....0..0..0....0..5..0....0..0..4....2..0..0

CROSSREFS

Cf. A186861.

Sequence in context: A254694 A279983 A187862 * A135239 A046043 A138480

Adjacent sequences:  A186861 A186862 A186863 * A186865 A186866 A186867

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2011

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)