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A187299 Number of 4-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions. 1
0, 0, 54, 196, 480, 876, 1398, 2036, 2790, 3660, 4646, 5748, 6966, 8300, 9750, 11316, 12998, 14796, 16710, 18740, 20886, 23148, 25526, 28020, 30630, 33356, 36198, 39156, 42230, 45420, 48726, 52148, 55686, 59340, 63110, 66996, 70998, 75116, 79350, 83700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 4 of A187296.

LINKS

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

FORMULA

Empirical: a(n) = 58*n^2 - 232*n + 180 for n>5.

Conjectures from Colin Barker, Apr 23 2018: (Start)

G.f.: 2*x^3*(27 + 17*x + 27*x^2 - 15*x^3 + 7*x^4 - 5*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:

..1..0..0..0....0..0..0..0....0..0..1..0....0..0..0..0....0..0..0..0

..0..0..0..0....0..0..0..0....0..0..0..0....0..2..1..0....2..4..3..0

..2..4..3..0....1..3..2..4....4..3..2..0....0..4..0..0....1..0..0..0

..0..0..0..0....0..0..0..0....0..0..0..0....0..3..0..0....0..0..0..0

CROSSREFS

Cf. A187296.

Sequence in context: A044980 A248598 A157428 * A288626 A124007 A221867

Adjacent sequences: A187296 A187297 A187298 * A187300 A187301 A187302

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 08 2011

STATUS

approved

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Last modified November 29 08:47 EST 2022. Contains 358422 sequences. (Running on oeis4.)