OFFSET
0,2
LINKS
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+10)^2 - 10^2 = n*(n+20), n>=0.
G.f.: x*(21-19*x)/(1-x)^3.
a(n) = 2*n + a(n-1) + 19 (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(20)/20 = A001008(20)/A102928(20) = 11167027/62078016, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 155685007/4655851200. (End)
MAPLE
seq(sum(4*k-n, k=7..n), n=6..51); # Zerinvary Lajos, Feb 17 2008
MATHEMATICA
s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 21, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
PROG
(PARI) a(n)=n*(n+20) \\ Charles R Greathouse IV, Jan 21 2015
CROSSREFS
a(n-10), n>=11, tenth column (used for the n=10 series of the hydrogen atom) of triangle A120070.
For n*(n+18) see A098850.
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved