A187303 Number of 8-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.

0, 0, 72, 2028, 12778, 37124, 81362, 145100, 231552, 338044, 465734, 613212, 780752, 968044, 1175118, 1401948, 1648534, 1914876, 2200974, 2506828, 2832438, 3177804, 3542926, 3927804, 4332438, 4756828, 5200974, 5664876, 6148534, 6651948, 7175118

Offset: 1

Author

R. H. Hardin, Mar 08 2011

Keywords

• nonn

Comments

Row 8 of A187296.

Examples

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

Links

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

Crossrefs

Cf. A187296.

Formula

Empirical: a(n) = 9878*n^2 - 79388*n + 143388 for n>13.

Conjectures from Colin Barker, Apr 23 2018: (Start)

G.f.: 2*x^3*(36 + 906*x + 3455*x^2 + 2401*x^3 + 3148*x^4 - 196*x^5 + 1607*x^6 - 1337*x^7 + 579*x^8 - 705*x^9 + 137*x^10 - 155*x^11 + 15*x^12 - 13*x^13) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>16.

(End)