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

0,2

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).

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)

Mathematica

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

Prog

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

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.

Sequence in context: A219920 A219216 A042566 * A329306 A329307 A336088

Adjacent sequences: A132766 A132767 A132768 * A132770 A132771 A132772

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved