OFFSET
0,2
COMMENTS
18 times the n-th triangular number.
Numbers of the form 36*m^2 + 18*m, where m = 0,-1,1,-2,2,-3,3,... - Bruno Berselli, Apr 07 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: 18*x/(1-x)^3.
E.g.f.: 9*x*(x + 2)*exp(x). - G. C. Greubel, Aug 02 2017
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/9.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/9.
Product_{n>=1} (1 - 1/a(n)) = -(9/Pi)*cos(sqrt(13)*Pi/6).
Product_{n>=1} (1 + 1/a(n)) = (9/Pi)*cos(sqrt(5)*Pi/6). (End)
MATHEMATICA
Table[9 n (n + 1), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
PROG
(Magma) [0] cat [36*m^2+18*m where m is n*t: t in [-1, 1], n in [1..20]]; // Bruno Berselli, Apr 07 2013
(PARI) a(n)=9*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 03 2009
EXTENSIONS
a(35) inserted by R. J. Mathar, Aug 06 2009
STATUS
approved