A187861 Number of 6-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

0, 0, 846, 9932, 47962, 126397, 262409, 452766, 707541, 1017934, 1387600, 1813854, 2296696, 2836126, 3432144, 4084750, 4793944, 5559726, 6382096, 7261054, 8196600, 9188734, 10237456, 11342766, 12504664, 13723150, 14998224, 16329886, 17718136

Offset

1,3

Comments

Row 6 of A187857.

Links

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

Formula

Empirical: a(n) = 28294*n^2 - 224508*n + 433614 for n>9.

Conjectures from Colin Barker, Apr 26 2018: (Start)

G.f.: x^3*(846 + 7394*x + 20704*x^2 + 11461*x^3 + 17172*x^4 - 3232*x^5 + 10073*x^6 - 8800*x^7 + 3655*x^8 - 2685*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..0..0..0....5..0..6..0....0..3..2..6....0..0..1..0....0..0..0..1
..3..2..4..0....4..3..0..0....1..0..0..5....0..5..0..0....0..0..3..0
..0..1..0..0....0..0..2..0....0..0..0..4....3..2..4..0....6..5..2..0
..6..5..0..0....1..0..0..0....0..0..0..0....6..0..0..0....0..0..4..0

Crossrefs

Cf. A187857.

Sequence in context: A323253 A160212 A188296 * A280484 A203335 A252253

Adjacent sequences: A187858 A187859 A187860 * A187862 A187863 A187864

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved