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

0,2

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 + 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)

Example

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

Mathematica

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

Prog

(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

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.

Sequence in context: A087807 A044100 A044481 * A029493 A063321 A176660

Adjacent sequences: A132761 A132762 A132763 * A132765 A132766 A132767

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved