A132763 a(n) = n*(n+21).

0, 22, 46, 72, 100, 130, 162, 196, 232, 270, 310, 352, 396, 442, 490, 540, 592, 646, 702, 760, 820, 882, 946, 1012, 1080, 1150, 1222, 1296, 1372, 1450, 1530, 1612, 1696, 1782, 1870, 1960, 2052, 2146, 2242, 2340, 2440, 2542, 2646, 2752, 2860, 2970, 3082, 3196, 3312

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 + 21).

a(n) = 2*n + a(n-1) + 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=22, a(2)=46, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 25 2014

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(21)/21 = A001008(21)/A102928(21) = 18858053/108636528, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/21 - 166770367/4888643760. (End)

From Stefano Spezia, Jan 30 2021: (Start)

O.g.f.: 2*x*(11 - 10*x)/(1 - x)^3.

E.g.f.: x*(22 + x)*exp(x). (End)

Mathematica

Table[n(n+21), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 22, 46}, 50] (* Harvey P. Dale, May 25 2014 *)

Prog

(PARI) a(n)=n*(n+21) \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [n*(n+21) for n in (0..50)] # G. C. Greubel, Mar 14 2022

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132764, A132765, A132766, A132767.

Sequence in context: A335297 A158862 A161666 * A250723 A044099 A044480

Adjacent sequences: A132760 A132761 A132762 * A132764 A132765 A132766

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved