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A187290 Number of 5-step one or two space at a time rook's tours on an n X n board summed over all starting positions. 1
0, 0, 720, 4576, 13640, 28224, 48232, 73408, 103692, 139056, 179500, 225024, 275628, 331312, 392076, 457920, 528844, 604848, 685932, 772096, 863340, 959664, 1061068, 1167552, 1279116, 1395760, 1517484, 1644288, 1776172, 1913136, 2055180, 2202304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 5 of A187286.

LINKS

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

FORMULA

Empirical: a(n) = 2540*n^2 - 12896*n + 14016 for n>7.

Conjectures from Colin Barker, Apr 22 2018: (Start)

G.f.: 4*x^3*(180 + 604*x + 518*x^2 + 78*x^3 - 24*x^4 - 64*x^5 - 15*x^6 - 7*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 5 1 0    0 0 2 1    5 0 0 0    3 0 4 5    0 0 1 0

  0 0 0 0    0 0 0 0    4 3 0 0    2 0 0 0    0 0 2 0

  0 4 2 3    5 4 3 0    0 0 0 0    0 0 0 0    5 4 3 0

  0 0 0 0    0 0 0 0    0 2 0 1    1 0 0 0    0 0 0 0

CROSSREFS

Cf. A187286.

Sequence in context: A202095 A233787 A280920 * A218487 A053625 A052793

Adjacent sequences:  A187287 A187288 A187289 * A187291 A187292 A187293

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 08 2011

STATUS

approved

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Last modified November 27 15:36 EST 2021. Contains 349394 sequences. (Running on oeis4.)