A132764 a(n) = n*(n+22).

0, 23, 48, 75, 104, 135, 168, 203, 240, 279, 320, 363, 408, 455, 504, 555, 608, 663, 720, 779, 840, 903, 968, 1035, 1104, 1175, 1248, 1323, 1400, 1479, 1560, 1643, 1728, 1815, 1904, 1995, 2088, 2183, 2280, 2379, 2480, 2583, 2688, 2795, 2904, 3015, 3128, 3243, 3360

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• easy
• nonn

Examples

			a(1)=2*1+0+21=23; a(2)=2*2+23+21=48; a(3)=2*3+48+21=75. - _Vincenzo Librandi_, Aug 03 2010
		

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, A132763, A132765, A132766, A132767.

Programs

Mathematica

Table[n(n+22),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,23,48},50] (* Harvey P. Dale, May 02 2012 *)

PARI

a(n)=n*(n+22) \\ Charles R Greathouse IV, Oct 07 2015

Sage

[n*(n+22) for n in (0..50)] # G. C. Greubel, Mar 14 2022

Formula

a(n) = n*(n + 22).

a(n) = 2*n + a(n-1) + 21 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=23, a(2)=48, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 02 2012

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(22)/22 = A001008(22)/A102928(22) = 19093197/113809696, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 156188887/5121436320. (End)

From G. C. Greubel, Mar 14 2022: (Start)

G.f.: x*(23 - 21*x)/(1-x)^3.

E.g.f.: x*(23 + x)*exp(x). (End)