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) + 18 for n > 0, a(0) = 0. - Vincenzo Librandi, Aug 03 2010
From Chai Wah Wu, Dec 17 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: 2*x*(10 - 9*x)/(1-x)^3. (End)
a(n) = 2*A051942(n+9). - R. J. Mathar, Sep 05 2018
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(19)/19 = A001008(19)/A102928(19) = 275295799/1474352880, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/19 - 33464927/884611728. (End)
E.g.f.: x*(20 + x)*exp(x). - G. C. Greubel, Mar 14 2022
MATHEMATICA
Table[n (n + 19), {n, 0, 50}] (* Bruno Berselli, Sep 05 2018 *)
LinearRecurrence[{3, -3, 1}, {0, 20, 42}, 60] (* Harvey P. Dale, Jun 03 2021 *)
PROG
(PARI) a(n)=n*(n+19) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+19) for n in (0..50)] # G. C. Greubel, Mar 14 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved