A187299 Number of 4-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, 54, 196, 480, 876, 1398, 2036, 2790, 3660, 4646, 5748, 6966, 8300, 9750, 11316, 12998, 14796, 16710, 18740, 20886, 23148, 25526, 28020, 30630, 33356, 36198, 39156, 42230, 45420, 48726, 52148, 55686, 59340, 63110, 66996, 70998, 75116, 79350, 83700

Offset

1,3

Comments

Row 4 of A187296.

Links

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

Formula

Empirical: a(n) = 58*n^2 - 232*n + 180 for n>5.

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

G.f.: 2*x^3*(27 + 17*x + 27*x^2 - 15*x^3 + 7*x^4 - 5*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Cf. A187296.

Sequence in context: A044980 A248598 A157428 * A288626 A124007 A221867

Adjacent sequences: A187296 A187297 A187298 * A187300 A187301 A187302

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved