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

1,3

Comments

Row 8 of A187296.

Links

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

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)

Example

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

Crossrefs

Cf. A187296.

Sequence in context: A008659 A263974 A344029 * A268994 A347566 A277532

Adjacent sequences: A187300 A187301 A187302 * A187304 A187305 A187306

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved