A187611 Number of 7-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

0, 0, 0, 0, 48, 616, 2936, 8530, 17611, 32086, 51955, 76258, 105978, 140386, 179482, 223266, 271738, 324898, 382746, 445282, 512506, 584418, 661018, 742306, 828282, 918946, 1014298, 1114338, 1219066, 1328482, 1442586, 1561378, 1684858, 1813026

Offset

1,5

Comments

Row 7 of A187606.

Links

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

Formula

Empirical: a(n) = 2344*n^2 - 28880*n + 85282 for n>11.

Conjectures from Colin Barker, Apr 25 2018: (Start)

G.f.: x^5*(48 + 472*x + 1232*x^2 + 1522*x^3 + 213*x^4 + 1907*x^5 - 960*x^7 + 983*x^8 - 729*x^9) / (1 - x)^3.

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

(End)

Example

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

Crossrefs

Cf. A187606.

Sequence in context: A179404 A171343 A151624 * A362235 A160286 A008658

Adjacent sequences: A187608 A187609 A187610 * A187612 A187613 A187614

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved