oeis.org

A132763 - OEIS

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

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

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)

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

(Sage) [n*(n+21) for n in (0..50)] # G. C. Greubel, Mar 14 2022