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A193828
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Even generalized pentagonal numbers.
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3
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0, 2, 12, 22, 26, 40, 70, 92, 100, 126, 176, 210, 222, 260, 330, 376, 392, 442, 532, 590, 610, 672, 782, 852, 876, 950, 1080, 1162, 1190, 1276, 1426, 1520, 1552, 1650, 1820, 1926, 1962, 2072, 2262, 2380, 2420, 2542, 2752, 2882, 2926, 3060, 3290, 3432, 3480
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: -2*x*(x^2-x+1)*(x^2+4*x+1)/((x-1)^3*(x^2+1)^2). - Colin Barker, Sep 12 2012
Sum_{n>=1} 1/a(n) = 6 - (1+4/sqrt(3))*Pi/2. - Amiram Eldar, Mar 18 2022
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MATHEMATICA
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CoefficientList[Series[-2*x*(x^2 - x + 1)*(x^2 + 4*x + 1)/((x - 1)^3*(x^2 + 1)^2), {x, 0, 50}], x] (* G. C. Greubel, Jun 06 2017 *)
LinearRecurrence[{3, -5, 7, -7, 5, -3, 1}, {0, 2, 12, 22, 26, 40, 70}, 50] (* Harvey P. Dale, Apr 09 2019 *)
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PROG
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(PARI) my(x='x+O('x^50)); concat([0], Vec(-2*x*(x^2-x+1)*(x^2+4*x+1)/((x-1)^3*(x^2+1)^2))) \\ G. C. Greubel, Jun 06 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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