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.

0, 0, 16032, 292776, 1400168, 3807828, 7700944, 13082348, 19910456, 28160124, 37824352, 48902340, 61394088, 75299596, 90618864, 107351892, 125498680, 145059228, 166033536, 188421604, 212223432, 237439020, 264068368, 292111476

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