A187302 Number of 7-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, 108, 1368, 6264, 15596, 31172, 52256, 79634, 112568, 151266, 195512, 245332, 300704, 361628, 428104, 500132, 577712, 660844, 749528, 843764, 943552, 1048892, 1159784, 1276228, 1398224, 1525772, 1658872, 1797524, 1941728, 2091484, 2246792

Offset

1,3

Comments

Row 7 of A187296.

Links

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

Formula

Empirical: a(n) = 2776*n^2 - 19580*n + 30728 for n>11.

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

G.f.: 2*x^3*(54 + 522*x + 1242*x^2 + 400*x^3 + 904*x^4 - 368*x^5 + 393*x^6 - 369*x^7 + 104*x^8 - 108*x^9 + 13*x^10 - 11*x^11) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

(End)

Example

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

Crossrefs

Cf. A187296.

Sequence in context: A202092 A202484 A096953 * A269277 A115135 A202309

Adjacent sequences: A187299 A187300 A187301 * A187303 A187304 A187305

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved