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) = 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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved