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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A242296 A223507 A135590 * A250137 A109399 A111029

Adjacent sequences:  A187856 A187857 A187858 * A187860 A187861 A187862

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 14 2011

STATUS

approved

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Last modified December 3 17:23 EST 2021. Contains 349467 sequences. (Running on oeis4.)