A132771 a(n) = n*(n + 29).

0, 30, 62, 96, 132, 170, 210, 252, 296, 342, 390, 440, 492, 546, 602, 660, 720, 782, 846, 912, 980, 1050, 1122, 1196, 1272, 1350, 1430, 1512, 1596, 1682, 1770, 1860, 1952, 2046, 2142, 2240, 2340, 2442, 2546, 2652, 2760, 2870, 2982, 3096, 3212, 3330, 3450, 3572

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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) = 2*n + a(n-1) + 28 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(29)/29 = A001008(29)/A102928(29) = 9227046511387/67543597321200, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/29 - 236266661971/9649085331600. (End)

From G. C. Greubel, Mar 13 2022: (Start)

G.f.: 2*(15*x - 14*x^2)/(1-x)^3.

E.g.f.: x*(30 + x)*exp(x). (End)

Mathematica

Table[n(n+29), {n, 0, 50}] (* Bruno Berselli, Apr 03 2015 *)

Prog

(PARI) a(n)=n*(n+29) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+29) for n in (0..50)] # G. C. Greubel, Mar 13 2022

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.

Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.

Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.

Sequence in context: A042796 A042798 A320705 * A326158 A300790 A175259

Adjacent sequences: A132768 A132769 A132770 * A132772 A132773 A132774

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved