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

0,2

Links

Table of n, a(n) for n=0..43.

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).

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)

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 *)

Prog

(PARI) a(n)=n*(n+15) \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A001477, A002378, A056121, A056126, A098849, A120071, A132761, A132765.

Sequence in context: A245664 A091216 A350522 * A209377 A203446 A153819

Adjacent sequences: A132757 A132758 A132759 * A132761 A132762 A132763

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved