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A187854 Number of 6-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, 16032, 292776, 1400168, 3807828, 7700944, 13082348, 19910456, 28160124, 37824352, 48902340, 61394088, 75299596, 90618864, 107351892, 125498680, 145059228, 166033536, 188421604, 212223432, 237439020, 264068368, 292111476 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 6 of A187850.

LINKS

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

FORMULA

Empirical: a(n) = 706880*n^2 - 5180252*n + 9274644 for n>9.

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

G.f.: 4*x^3*(4008 + 61170*x + 142484*x^2 + 117405*x^3 + 46297*x^4 + 708*x^5 - 10396*x^6 - 6286*x^7 - 1750*x^8 - 200*x^9) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)

EXAMPLE

Some solutions for 4 X 4:

..0..5..4..0....0..0..0..0....0..0..0..0....0..4..0..6....0..0..2..0

..1..6..3..0....0..4..0..0....0..1..4..6....0..0..5..0....0..0..3..1

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

..0..0..0..0....1..2..6..0....0..3..0..0....0..0..0..2....6..4..0..0

CROSSREFS

Cf. A187850.

Sequence in context: A218642 A151811 A151877 * A204942 A163112 A202420

Adjacent sequences:  A187851 A187852 A187853 * A187855 A187856 A187857

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 14 2011

STATUS

approved

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Last modified October 21 10:52 EDT 2021. Contains 348150 sequences. (Running on oeis4.)