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) + 27, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)
G.f.: x*(29 - 27*x)/(1-x)^3. - Harvey P. Dale, Aug 03 2021
E.g.f.: x*(29 + x)*exp(x). - G. C. Greubel, Mar 13 2022
MATHEMATICA
#(#+28)&/@Range[0, 50] (* or *) LinearRecurrence[{3, -3, 1}, {0, 29, 60}, 50] (* Harvey P. Dale, Apr 30 2018 *)
PROG
(PARI) a(n)=n*(n+28) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+28) for n in (0..50)] # G. C. Greubel, Mar 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved