A187860 Number of 5-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, 486, 3320, 11986, 26836, 50378, 81124, 120051, 166504, 220483, 281988, 351019, 427576, 511659, 603268, 702403, 809064, 923251, 1044964, 1174203, 1310968, 1455259, 1607076, 1766419, 1933288, 2107683, 2289604, 2479051, 2676024, 2880523

Offset

1,3

Comments

Row 5 of A187857.

Links

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

Formula

Empirical: a(n) = 3763*n^2 - 25044*n + 40644 for n>7.

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

G.f.: x^3*(486 + 1862*x + 3484*x^2 + 352*x^3 + 2508*x^4 - 1488*x^5 + 977*x^6 - 655*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

Example

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

Crossrefs

Cf. A187857.

Sequence in context: A249227 A130181 A158325 * A205240 A206146 A128969

Adjacent sequences: A187857 A187858 A187859 * A187861 A187862 A187863

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved