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A128214
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Expansion of (1+2x+3x^2)/(1+x+x^2)^2.
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3
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1, 0, 0, -2, 3, 0, -5, 6, 0, -8, 9, 0, -11, 12, 0, -14, 15, 0, -17, 18, 0, -20, 21, 0, -23, 24, 0, -26, 27, 0, -29, 30, 0, -32, 33, 0, -35, 36, 0, -38, 39, 0, -41, 42, 0, -44, 45, 0, -47, 48, 0, -50, 51, 0, -53, 54, 0, -56, 57, 0, -59, 60, 0, -62, 63, 0, -65
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1+2x+3x^2)/(1+x+x^2)^2.
a(n) = (1-n)*cos(2*Pi*n/3)+(n-1)*sin(2*Pi*n/3)/sqrt(3).
a(n) + 2*a(n-1) + 3*a(n-2) + 2*a(n-3) + a(n-4) = 0.
a(n) = (n-1) * ((n-2)^2 mod 3) * (-1)^floor((2n-2)/3). (End)
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MATHEMATICA
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CoefficientList[Series[(1 + 2 x + 3 x^2)/(1 + x + x^2)^2, {x, 0, 50}], x] (* Wesley Ivan Hurt, Mar 15 2015 *)
LinearRecurrence[{-2, -3, -2, -1}, {1, 0, 0, -2}, 70] (* Harvey P. Dale, Jul 16 2021 *)
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PROG
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(PARI) Vec((1+2*x+3*x^2)/(1+x+x^2)^2 + O(x^80)) \\ Michel Marcus, Mar 16 2015
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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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EXTENSIONS
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STATUS
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approved
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