A132768 a(n) = n*(n + 26).

0, 27, 56, 87, 120, 155, 192, 231, 272, 315, 360, 407, 456, 507, 560, 615, 672, 731, 792, 855, 920, 987, 1056, 1127, 1200, 1275, 1352, 1431, 1512, 1595, 1680, 1767, 1856, 1947, 2040, 2135, 2232, 2331, 2432, 2535, 2640, 2747, 2856, 2967, 3080, 3195, 3312, 3431

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) = n*(n + 26).

a(n) = 2*n + a(n-1) + 25, with a(0)=0. - Vincenzo Librandi, Aug 03 2010

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(26)/26 = A001008(26)/A102928(26) = 34395742267/232016584800, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 18051406831/696049754400. (End)

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

G.f.: x*(27 - 25*x)/(1-x)^3.

E.g.f.: x*(27 + x)*exp(x). (End)

Mathematica

Table[n(n+26), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 27, 56}, 50] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(PARI) a(n)=n*(n+26) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+26) 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.

Sequence in context: A042452 A042454 A042456 * A352266 A053180 A080864

Adjacent sequences: A132765 A132766 A132767 * A132769 A132770 A132771

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved