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A187289
Number of 4-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
1
0, 8, 288, 1256, 3084, 5712, 9120, 13288, 18216, 23904, 30352, 37560, 45528, 54256, 63744, 73992, 85000, 96768, 109296, 122584, 136632, 151440, 167008, 183336, 200424, 218272, 236880, 256248, 276376, 297264, 318912, 341320, 364488, 388416
OFFSET
1,2
COMMENTS
Row 4 of A187286.
LINKS
FORMULA
Empirical: a(n) = 380*n^2 - 1532*n + 1224 for n>5.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^2*(2 + 66*x + 104*x^2 + 43*x^3 - 15*x^4 - 5*x^5 - 5*x^6) / (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..1..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..1..0..0
..0..2..0..0....0..0..4..0....0..0..0..0....0..0..1..0....3..2..0..0
..0..4..0..0....0..0..0..0....2..3..0..0....0..0..2..3....4..0..0..0
..0..3..0..0....0..1..3..2....0..4..0..0....0..0..0..4....0..0..0..0
CROSSREFS
Cf. A187286.
Sequence in context: A348122 A060355 A060859 * A187191 A054607 A254408
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved