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A274616
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Maximal number of non-attacking queens on a right triangular board with n cells on each side.
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9
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0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47
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OFFSET
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0,4
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COMMENTS
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REFERENCES
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Paul Vanderlind, Richard K. Guy, and Loren C. Larson, The Inquisitive Problem Solver, MAA, 2002. See Problem 252, pages 67, 87, 198 and 276.
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LINKS
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FORMULA
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Except for n=4, this is round(2n/3).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
G.f.: x*(1+x^2-x^3)*(1+x^4)/((1-x)^2*(1+x+x^2)). (End)
a(n) = 2*(3*n + sqrt(3)*sin((2*Pi*n)/3)) / 9. - Colin Barker, Mar 08 2017
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EXAMPLE
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n=3:
OOX
XO
O
n=4:
OOOX
OXO
OO
O
n=5:
OOOOX
OOXO
XOO
OO
O
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MATHEMATICA
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CoefficientList[Series[x*(1 +x^2 -x^3)*(1 +x^4)/((1-x)^2*(1+x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Jul 03 2016 *)
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PROG
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(PARI) concat(0, Vec(x*(1+x^2-x^3)*(1+x^4)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jul 02 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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