login
A187288
Number of 3-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, 108, 328, 672, 1128, 1696, 2376, 3168, 4072, 5088, 6216, 7456, 8808, 10272, 11848, 13536, 15336, 17248, 19272, 21408, 23656, 26016, 28488, 31072, 33768, 36576, 39496, 42528, 45672, 48928, 52296, 55776, 59368, 63072, 66888, 70816, 74856, 79008
OFFSET
1,2
COMMENTS
Row 3 of A187286.
LINKS
FORMULA
Empirical: a(n) = 56*n^2 - 160*n + 72 for n>3.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^2*(2 + 21*x + 7*x^2 + x^3 - 3*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....0..0..0..0....0..0..0..0....3..0..0..0....0..0..3..2
..2..0..0..0....0..0..0..0....0..0..0..0....2..0..1..0....0..0..0..1
..1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....3..0..2..0....2..0..3..0....0..0..0..0....0..0..0..0
CROSSREFS
Cf. A187286.
Sequence in context: A239985 A274892 A105261 * A275134 A187190 A099762
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved