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+8)^2 - 8^2 = n*(n + 16), n>=0.
G.f.: x*(17 - 15*x)/(1-x)^3.
a(n) = a(n-1) + 2*n + 15 (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*(17 + x)*exp(x). (End)
From Amiram Eldar, Jan 15 2021: (Start)
Sum_{n>=1} 1/a(n) = H(16)/16 = A001008(16)/A102928(16) = 2436559/11531520, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 95549/2306304. (End)
MAPLE
seq(n*(n+16), n=0..55); # Emeric Deutsch, Mar 26 2005
a:=n->sum(n, j=17..n): seq(a(n), n=16..63); # Zerinvary Lajos, Feb 17 2008
MATHEMATICA
s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 17, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
LinearRecurrence[{3, -3, 1}, {0, 17, 36}, 50] (* G. C. Greubel, Jul 29 2016 *)
Table[n(n+16), {n, 0, 50}] (* Harvey P. Dale, Jul 18 2024 *)
PROG
(PARI) a(n)=n*(n+16) \\ Charles R Greathouse IV, Jul 30 2016
CROSSREFS
a(n-8), n>=9, eighth column (used for the n=8 series of the hydrogen atom) of triangle A120070.
KEYWORD
nonn,easy
AUTHOR
Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 26 2005
STATUS
approved