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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A072408 A318587 A302722

Adjacent sequences:  A187855 A187856 A187857 * A187859 A187860 A187861

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 14 2011

STATUS

approved

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)