A132770 a(n) = n*(n + 28).

0, 29, 60, 93, 128, 165, 204, 245, 288, 333, 380, 429, 480, 533, 588, 645, 704, 765, 828, 893, 960, 1029, 1100, 1173, 1248, 1325, 1404, 1485, 1568, 1653, 1740, 1829, 1920, 2013, 2108, 2205, 2304, 2405, 2508, 2613, 2720, 2829, 2940, 3053, 3168, 3285, 3404, 3525

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) + 27, with a(0)=0. - Vincenzo Librandi, Aug 03 2010

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)

G.f.: x*(29 - 27*x)/(1-x)^3. - Harvey P. Dale, Aug 03 2021

E.g.f.: x*(29 + x)*exp(x). - G. C. Greubel, Mar 13 2022

Mathematica

#(#+28)&/@Range[0, 50] (* or *) LinearRecurrence[{3, -3, 1}, {0, 29, 60}, 50] (* Harvey P. Dale, Apr 30 2018 *)

Prog

(PARI) a(n)=n*(n+28) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+28) for n in (0..50)] # G. C. Greubel, Mar 13 2022

Crossrefs

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

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

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

Sequence in context: A042678 A042680 A286005 * A141111 A122114 A173032

Adjacent sequences: A132767 A132768 A132769 * A132771 A132772 A132773

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved