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A132771
a(n) = n*(n + 29).
3
0, 30, 62, 96, 132, 170, 210, 252, 296, 342, 390, 440, 492, 546, 602, 660, 720, 782, 846, 912, 980, 1050, 1122, 1196, 1272, 1350, 1430, 1512, 1596, 1682, 1770, 1860, 1952, 2046, 2142, 2240, 2340, 2442, 2546, 2652, 2760, 2870, 2982, 3096, 3212, 3330, 3450, 3572
OFFSET
0,2
LINKS
FORMULA
a(n) = 2*n + a(n-1) + 28 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(29)/29 = A001008(29)/A102928(29) = 9227046511387/67543597321200, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/29 - 236266661971/9649085331600. (End)
From G. C. Greubel, Mar 13 2022: (Start)
G.f.: 2*(15*x - 14*x^2)/(1-x)^3.
E.g.f.: x*(30 + x)*exp(x). (End)
MATHEMATICA
Table[n(n+29), {n, 0, 50}] (* Bruno Berselli, Apr 03 2015 *)
LinearRecurrence[{3, -3, 1}, {0, 30, 62}, 50] (* Harvey P. Dale, Oct 18 2024 *)
PROG
(PARI) a(n)=n*(n+29) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+29) for n in (0..50)] # G. C. Greubel, Mar 13 2022
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved