A187178 Number of 8-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

0, 0, 0, 0, 0, 0, 280, 1784, 5944, 14072, 27104, 45288, 68400, 96048, 128064, 164424, 205128, 250176, 299568, 353304, 411384, 473808, 540576, 611688, 687144, 766944, 851088, 939576, 1032408, 1129584, 1231104, 1336968, 1447176, 1561728, 1680624

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 8 of A187172.

Examples

			Some solutions for 7 X 7:
..0..0..0..4..0..0..0....0..0..0..0..4..0..0....0..0..0..0..0..0..0
..0..5..0..0..0..0..0....0..0..3..0..0..0..0....0..0..0..0..8..0..0
..0..0..0..0..3..0..0....2..0..0..0..0..5..0....0..0..7..0..0..0..0
..0..0..6..0..0..0..0....0..0..0..8..0..0..0....6..0..0..0..0..1..0
..7..0..0..0..0..2..0....0..1..0..0..0..0..6....0..0..0..4..0..0..0
..0..0..0..1..0..0..0....0..0..0..0..7..0..0....0..5..0..0..0..0..2
..0..8..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..3..0..0
		

Links

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

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 2172*n^2 - 30972*n + 103944 for n>13.

Empirical g.f.: 8*x^7*(35 + 118*x + 179*x^2 + 164*x^3 + 117*x^4 + 31*x^5 - 28*x^6 - 49*x^7 - 21*x^8 - 3*x^9) / (1 - x)^3. - Colin Barker, Apr 22 2018