A132769 a(n) = n*(n + 27).

0, 28, 58, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 520, 574, 630, 688, 748, 810, 874, 940, 1008, 1078, 1150, 1224, 1300, 1378, 1458, 1540, 1624, 1710, 1798, 1888, 1980, 2074, 2170, 2268, 2368, 2470, 2574, 2680, 2788, 2898, 3010, 3124, 3240, 3358, 3478

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• 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).

Crossrefs

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

Cf. A028569, A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759.

Cf. A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768.

Cf. A132756.

Programs

Mathematica

Table[n(n+27),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,28,58},50] (* Harvey P. Dale, Oct 14 2012 *)

PARI

a(n)=n*(n+27) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 2*n + a(n-1) + 26, with a(0)=0. - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=28, a(2)=58; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 14 2012

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(27)/27 = A001008(27)/A102928(27) = 312536252003/2168462696400, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/27 - 57128792093/2168462696400. (End)

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: 2*x*(14 - 13*x)/(1 - x)^3.

E.g.f.: exp(x)*x*(28 + x).

a(n) = 2*A132756(n). (End)