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A166592
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Hankel transform of A166588(n-1).
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2
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0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3
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OFFSET
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0,3
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COMMENTS
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Hankel transform of 0,1,2,2,3,3,5,5,10,10,... is -a(n).
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LINKS
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FORMULA
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G.f.: x(1+3x+x^2)/(1-x^2+x^4).
a(n) = (1-sqrt(3))*sin(5*Pi*n/6)+(1+sqrt(3))*sin(Pi*n/6).
a(n+12) = a(n).
a(n) = a(n-2) - a(n-4). (End)
E.g.f.: 2*sin(x/2)*(sqrt(3)*sinh(sqrt(3)*x/2) + cosh(sqrt(3)*x/2)). - Ilya Gutkovskiy, May 18 2016
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MATHEMATICA
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CoefficientList[Series[x (1 + 3 x + x^2)/(1 - x^2 + x^4), {x, 0, 10}], x] (* or *) LinearRecurrence[{0, 1, 0, -1}, {0, 1, 3, 2}, 25] (* G. C. Greubel, May 18 2016 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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