A132760 a(n) = n*(n+15).
0, 16, 34, 54, 76, 100, 126, 154, 184, 216, 250, 286, 324, 364, 406, 450, 496, 544, 594, 646, 700, 756, 814, 874, 936, 1000, 1066, 1134, 1204, 1276, 1350, 1426, 1504, 1584, 1666, 1750, 1836, 1924, 2014, 2106, 2200, 2296, 2394, 2494
Offset: 0
Links
- Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
s=0;lst={};Do[s+=n;AppendTo[lst,s],{n,16,6!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *) Table[n(n+15),{n,0,60}] (* or *) LinearRecurrence[{3,-3,1},{0,16,34},60] (* Harvey P. Dale, Jan 20 2019 *) -
PARI
a(n)=n*(n+15) \\ Charles R Greathouse IV, Sep 24 2015
Formula
a(n) = n*(n + 15).
a(n) = 2*A056121(n). - Reinhard Zumkeller, Mar 20 2009
a(n) = 2*n + a(n-1) + 14 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
G.f.: 2*x*(-8+7*x)/(x-1)^3. - R. J. Mathar, Jul 14 2012
Sum_{n>=1} 1/a(n) = 1195757/5405400 = 0.22121526621... - R. J. Mathar, Jul 14 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/15 - 52279/1081080. - Amiram Eldar, Jan 15 2021
From Elmo R. Oliveira, Dec 12 2024: (Start)
E.g.f.: exp(x)*x*(16 + x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)