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

Author

Omar E. Pol, Aug 28 2007

Keywords

• easy
• nonn

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).

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.

Programs

Mathematica

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

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

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)