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 A033579 Four times pentagonal numbers: a(n) = 2*n*(3*n-1). 22

%I

%S 0,4,20,48,88,140,204,280,368,468,580,704,840,988,1148,1320,1504,1700,

%T 1908,2128,2360,2604,2860,3128,3408,3700,4004,4320,4648,4988,5340,

%U 5704,6080,6468,6868,7280,7704,8140,8588,9048,9520,10004,10500,11008,11528,12060

%N Four times pentagonal numbers: a(n) = 2*n*(3*n-1).

%C Subsequence of A062717: A010052(6*a(n)+1) = 1. - _Reinhard Zumkeller_, Feb 21 2011

%C 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

%H Ivan Panchenko, <a href="/A033579/b033579.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pentagonal_number">Pentagonal number</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 4*n*(3*n-1)/2 = 6*n^2 - 2*n = 4*A000326(n). - _Omar E. Pol_, Dec 11 2008

%F a(n) = 2*A049450(n). - _Omar E. Pol_, Dec 13 2008

%F a(n) = 12*n+a(n-1)-8 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 05 2010

%F a(n) = A014642(n)/2. - _Omar E. Pol_, Aug 19 2011

%F G.f.: x*(4+8*x)/(1-3*x+3*x^2-x^3). - _Colin Barker_, Jan 06 2012

%F a(n) = A191967(2*n). - _Reinhard Zumkeller_, Jul 07 2012

%F a(n) = A181617(n+1) - A181617(n). - _J. M. Bergot_, Jun 28 2013

%F a(n) = (A174371(n) - 1)/6. - _Miquel Cerda_, Jul 28 2016

%F From _Ilya Gutkovskiy_, Jul 28 2016: (Start)

%F E.g.f.: 2*x*(2 + 3*x)*exp(x).

%F a(n+1) = Sum_{k=0..n} A017569(k).

%F Sum_{i>0} 1/a(i) = (9*log(3) - sqrt(3)*Pi)/12 = 0.3705093754425278... (End)

%t 4 PolygonalNumber[5, Range[0, 45]] (* _Michael De Vlieger_, Aug 02 2016, Version 10.4 *)

%o (PARI) a(n)=2*n*(3*n-1) \\ _Charles R Greathouse IV_, Jun 28 2013

%Y Cf. A049450, A014642, A033580, A186423, A000326, A001318, A033579, A033581.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Michel Marcus_, Mar 04 2014

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Last modified October 22 17:08 EDT 2018. Contains 316490 sequences. (Running on oeis4.)