A187858 Number of 3-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, 2, 81, 254, 578, 1030, 1610, 2318, 3154, 4118, 5210, 6430, 7778, 9254, 10858, 12590, 14450, 16438, 18554, 20798, 23170, 25670, 28298, 31054, 33938, 36950, 40090, 43358, 46754, 50278, 53930, 57710, 61618, 65654, 69818, 74110, 78530, 83078, 87754, 92558

Offset

1,2

Comments

Row 3 of A187857.

Links

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

Formula

Empirical: a(n) = 64*n^2 - 252*n + 238 for n>3.

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

G.f.: x^2*(2 + 75*x + 17*x^2 + 57*x^3 - 23*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

Example

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

Crossrefs

Cf. A187857.

Sequence in context: A056972 A051391 A041799 * A352742 A072408 A318587

Adjacent sequences: A187855 A187856 A187857 * A187859 A187860 A187861

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved