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A187851 Number of 3-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, 24, 304, 1056, 2312, 4048, 6264, 8960, 12136, 15792, 19928, 24544, 29640, 35216, 41272, 47808, 54824, 62320, 70296, 78752, 87688, 97104, 107000, 117376, 128232, 139568, 151384, 163680, 176456, 189712, 203448, 217664, 232360, 247536, 263192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 3 of A187850.

LINKS

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

FORMULA

Empirical: a(n) = 240*n^2 - 904*n + 832 for n>3.

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

G.f.: 8*x^2*(3 + 29*x + 27*x^2 + 4*x^3 - 3*x^4) / (1 - x)^3.

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

(End)

EXAMPLE

Some solutions for 4 X 4:

..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

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

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

..3..0..0..0....0..0..0..0....0..1..0..0....3..1..0..0....0..0..0..0

CROSSREFS

Cf. A187850.

Sequence in context: A000552 A233876 A171742 * A125436 A096821 A168303

Adjacent sequences:  A187848 A187849 A187850 * A187852 A187853 A187854

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 14 2011

STATUS

approved

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Last modified October 19 08:46 EDT 2021. Contains 348074 sequences. (Running on oeis4.)