A187300 Number of 5-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, 90, 416, 1208, 2400, 4092, 6208, 8766, 11752, 15166, 19008, 23278, 27976, 33102, 38656, 44638, 51048, 57886, 65152, 72846, 80968, 89518, 98496, 107902, 117736, 127998, 138688, 149806, 161352, 173326, 185728, 198558, 211816, 225502, 239616

Offset

1,3

Comments

Row 5 of A187296.

Links

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

Formula

Empirical: a(n) = 214*n^2 - 1080*n + 1152 for n>7.

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

G.f.: 2*x^3*(45 + 73*x + 115*x^2 - 33*x^3 + 50*x^4 - 38*x^5 + 9*x^6 - 7*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

Example

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

Crossrefs

Cf. A187296.

Sequence in context: A234984 A158490 A304618 * A237129 A250870 A284845

Adjacent sequences: A187297 A187298 A187299 * A187301 A187302 A187303

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved