OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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) = (n+9)^2 - 9^2 = n*(n + 18), n>=0.
G.f.: x*(19 - 17*x)/(1-x)^3.
a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010
From G. C. Greubel, Jul 29 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: x*(19 + x)*exp(x). (End)
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(18)/18 = A001008(18)/A102928(18) = 14274301/73513440, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1632341/44108064. (End)
MAPLE
seq(n*(n+18), n=0..52); # Emeric Deutsch, Mar 06 2005
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* G. C. Greubel, Jul 29 2016 *)
PROG
(PARI) a(n)=n*(n+18) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 06 2005
STATUS
approved