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A188781
Number of 6-turn bishop's tours on an n X n board summed over all starting positions.
1
0, 0, 0, 840, 15824, 112680, 516160, 1778608, 5082912, 12622640, 28225472, 58013112, 111476080, 202472856, 350897664, 584067552, 939135552, 1464903648, 2225144448, 3300867240, 4794722064, 6833735304, 9574980800, 13208790672
OFFSET
1,4
COMMENTS
Row 6 of A188777.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) -2*a(n-2) -12*a(n-3) +17*a(n-4) +8*a(n-5) -28*a(n-6) +8*a(n-7) +17*a(n-8) -12*a(n-9) -2*a(n-10) +4*a(n-11) -a(n-12).
From Vaclav Kotesovec, Sep 01 2012: (Start)
Empirical: G.f.: 8*x^4*(105 + 1558*x + 6383*x^2 + 13396*x^3 + 14367*x^4 + 9654*x^5 + 2937*x^6 + 528*x^7)/((1-x)^8*(1+x)^4).
Empirical: a(n) = -297/4 + 13961*n/28 - 32551*n^2/30 + 54158*n^3/45 - 4625*n^4/6 + 5189*n^5/18 - 872*n^6/15 + 1529*n^7/315 + (-1)^n*(297/4 - 439*n/4 + 99*n^2/2 - 7*n^3).
(End)
EXAMPLE
Some solutions for 4 X 4
..0..0..4..0....0..2..0..6....0..4..0..1....0..3..0..0....0..5..0..3
..0..3..0..1....1..0..4..0....5..0..2..0....2..0..4..0....6..0..4..0
..5..0..2..0....0..5..0..3....0..0..0..3....0..1..0..5....0..2..0..0
..0..6..0..0....0..0..0..0....0..0..6..0....0..0..6..0....1..0..0..0
CROSSREFS
Cf. A188777.
Sequence in context: A215230 A171260 A166758 * A166764 A226268 A218410
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 10 2011
STATUS
approved