A187301 Number of 6-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, 144, 884, 3006, 6520, 11896, 18832, 27478, 37696, 49508, 62896, 77860, 94400, 112516, 132208, 153476, 176320, 200740, 226736, 254308, 283456, 314180, 346480, 380356, 415808, 452836, 491440, 531620, 573376, 616708, 661616, 708100, 756160

Offset

1,3

Comments

Row 6 of A187296.

Links

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

Formula

Empirical: a(n) = 788*n^2 - 4736*n + 6256 for n>9.

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

G.f.: 2*x^3*(72 + 226*x + 393*x^2 + 5*x^3 + 235*x^4 - 151*x^5 + 75*x^6 - 69*x^7 + 11*x^8 - 9*x^9) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)

Example

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

Crossrefs

Cf. A187296.

Sequence in context: A234091 A234084 A223235 * A120089 A159748 A235957

Adjacent sequences: A187298 A187299 A187300 * A187302 A187303 A187304

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved