oeis.org

A132772 - OEIS

0, 31, 64, 99, 136, 175, 216, 259, 304, 351, 400, 451, 504, 559, 616, 675, 736, 799, 864, 931, 1000, 1071, 1144, 1219, 1296, 1375, 1456, 1539, 1624, 1711, 1800, 1891, 1984, 2079, 2176, 2275, 2376, 2479, 2584, 2691, 2800, 2911, 3024, 3139, 3256, 3375, 3496, 3619

FORMULA

G.f.: x*(31-29*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007

a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=31, a(2)=64, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 06 2015

Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)

E.g.f.: x*(31 + x)*exp(x). - G. C. Greubel, Mar 13 2022

MATHEMATICA

Table[n(n+30), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 31, 64}, 50] (* Harvey P. Dale, Mar 06 2015 *)

PROG

(Sage) [n*(n+30) for n in (0..50)] # G. C. Greubel, Mar 13 2022