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A033579
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Four times pentagonal numbers: a(n) = 2*n*(3*n-1).
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24
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0, 4, 20, 48, 88, 140, 204, 280, 368, 468, 580, 704, 840, 988, 1148, 1320, 1504, 1700, 1908, 2128, 2360, 2604, 2860, 3128, 3408, 3700, 4004, 4320, 4648, 4988, 5340, 5704, 6080, 6468, 6868, 7280, 7704, 8140, 8588, 9048, 9520, 10004, 10500, 11008, 11528, 12060
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 4, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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LINKS
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FORMULA
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G.f.: x*(4+8*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 06 2012
E.g.f.: 2*x*(2 + 3*x)*exp(x).
Sum_{i>0} 1/a(i) = (9*log(3) - sqrt(3)*Pi)/12 = 0.3705093754425278... (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(2*sqrt(3)) - log(2). - Amiram Eldar, Feb 20 2022
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [4*Binomial(3*n, 2)/3: n in [0..45]]; // G. C. Greubel, Oct 09 2019
(Sage) [4*binomial(3*n, 2)/3 for n in (0..45)] # G. C. Greubel, Oct 09 2019
(GAP) List([0..45], n-> 4*Binomial(3*n, 2)/3 ); # G. C. Greubel, Oct 09 2019
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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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EXTENSIONS
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STATUS
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approved
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