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A293006
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Expansion of 2*x^2*(x+1) / (2*x^3-3*x+1).
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4
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0, 0, 2, 8, 24, 68, 188, 516, 1412, 3860, 10548, 28820, 78740, 215124, 587732, 1605716, 4386900, 11985236, 32744276, 89459028, 244406612, 667731284, 1824275796, 4984014164, 13616579924, 37201188180, 101635536212, 277673448788, 758617970004, 2072582837588
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OFFSET
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0,3
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COMMENTS
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Number of associative, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n} that have annihilator elements.
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LINKS
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FORMULA
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a(n) = (-8 + (1-sqrt(3))^(1+n) + (1+sqrt(3))^(1+n)) / 6 for n>0.
a(n) = 3*a(n-1) - 2*a(n-2) for n>3.
(End)
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MAPLE
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f:= gfun:-rectoproc({a(n) = 3*a(n-1) - 2*a(n-3), a(0)=0, a(1)=0, a(2)=2, a(3)=8}, a(n), remember):
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MATHEMATICA
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PROG
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(PARI) concat(vector(2), Vec(2*x^2*(1 + x) / ((1 - x)*(1 - 2*x - 2*x^2)) + O(x^30))) \\ Colin Barker, Sep 28 2017
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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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