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A033579
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Four times pentagonal numbers: a(n) = 2*n*(3*n-1).
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22
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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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Subsequence of A062717: A010052(6*a(n)+1) = 1. - Reinhard Zumkeller, Feb 21 2011
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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Ivan Panchenko, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Pentagonal Number
Wikipedia, Pentagonal number
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 4*n*(3*n-1)/2 = 6*n^2 - 2*n = 4*A000326(n). - Omar E. Pol, Dec 11 2008
a(n) = 2*A049450(n). - Omar E. Pol, Dec 13 2008
a(n) = 12*n+a(n-1)-8 for n>0, a(0)=0. - Vincenzo Librandi, Aug 05 2010
a(n) = A014642(n)/2. - Omar E. Pol, Aug 19 2011
G.f.: x*(4+8*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 06 2012
a(n) = A191967(2*n). - Reinhard Zumkeller, Jul 07 2012
a(n) = A181617(n+1) - A181617(n). - J. M. Bergot, Jun 28 2013
a(n) = (A174371(n) - 1)/6. - Miquel Cerda, Jul 28 2016
From Ilya Gutkovskiy, Jul 28 2016: (Start)
E.g.f.: 2*x*(2 + 3*x)*exp(x).
a(n+1) = Sum_{k=0..n} A017569(k).
Sum_{i>0} 1/a(i) = (9*log(3) - sqrt(3)*Pi)/12 = 0.3705093754425278... (End)
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MATHEMATICA
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4 PolygonalNumber[5, Range[0, 45]] (* Michael De Vlieger, Aug 02 2016, Version 10.4 *)
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PROG
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(PARI) a(n)=2*n*(3*n-1) \\ Charles R Greathouse IV, Jun 28 2013
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CROSSREFS
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Cf. A049450, A014642, A033580, A186423, A000326, A001318, A033579, A033581.
Sequence in context: A163365 A145194 A164924 * A294630 A160799 A187274
Adjacent sequences: A033576 A033577 A033578 * A033580 A033581 A033582
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Michel Marcus, Mar 04 2014
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STATUS
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approved
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