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A187159
Number of 6-step one space at a time bishop's tours on an n X n board summed over all starting positions.
1
0, 0, 0, 56, 456, 1588, 3288, 5556, 8392, 11796, 15768, 20308, 25416, 31092, 37336, 44148, 51528, 59476, 67992, 77076, 86728, 96948, 107736, 119092, 131016, 143508, 156568, 170196, 184392, 199156, 214488, 230388, 246856, 263892, 281496, 299668
OFFSET
1,4
COMMENTS
Row 6 of A187155.
LINKS
FORMULA
Empirical: a(n) = 284*n^2 - 1992*n + 3316 for n>4.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^4*(14 + 72*x + 97*x^2 - 41*x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
EXAMPLE
Some solutions for 4 X 4:
..0..3..0..0....0..0..2..0....0..0..5..0....0..0..4..0....0..3..0..0
..4..0..2..0....0..1..0..3....0..4..0..6....0..5..0..3....2..0..4..0
..0..5..0..1....6..0..4..0....3..0..1..0....6..0..2..0....0..1..0..5
..0..0..6..0....0..5..0..0....0..2..0..0....0..1..0..0....0..0..6..0
CROSSREFS
Cf. A187155.
Sequence in context: A287702 A008447 A076647 * A220048 A257707 A067234
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2011
STATUS
approved