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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
OFFSET
1,3
COMMENTS
Row 5 of A187286.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved