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

Author

R. H. Hardin, Mar 14 2011

Keywords

• nonn

Comments

Row 6 of A187850.

Examples

			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
		

Links

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

Crossrefs

Cf. A187850.

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)