A187859 Number of 4-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, 216, 968, 2754, 5428, 9237, 14040, 19837, 26628, 34413, 43192, 52965, 63732, 75493, 88248, 101997, 116740, 132477, 149208, 166933, 185652, 205365, 226072, 247773, 270468, 294157, 318840, 344517, 371188, 398853, 427512, 457165, 487812

Offset

1,3

Comments

Row 4 of A187857.

Links

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

Formula

Empirical: a(n) = 497*n^2 - 2652*n + 3448 for n>5.

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

G.f.: x^3*(216 + 320*x + 498*x^2 - 146*x^3 + 247*x^4 - 141*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:
..0..0..0..0....3..2..4..0....0..0..0..0....0..4..0..0....0..0..0..4
..0..0..0..0....0..1..0..0....0..4..3..0....0..0..3..0....0..3..2..0
..4..3..2..0....0..0..0..0....2..1..0..0....1..0..2..0....0..0..0..1
..0..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

Crossrefs

Cf. A187857.

Sequence in context: A223507 A377845 A135590 * A250137 A109399 A111029

Adjacent sequences: A187856 A187857 A187858 * A187860 A187861 A187862

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved