OFFSET
0,2
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
a(n) = 34*A000217(n).
a(0)=0, a(1)=34, a(2)=102, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: 34*x/(1-x)^3. - Colin Barker, Jan 25 2012
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/17.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/17.
Product_{n>=1} (1 - 1/a(n)) = -(17/Pi)*cos(sqrt(21/17)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (17/Pi)*cos(sqrt(13/17)*Pi/2). (End)
MATHEMATICA
Table[17n(n+1), {n, 0, 40}] (* Harvey P. Dale, Apr 06 2011 *)
PROG
(PARI) a(n)=34*binomial(n+1, 2) \\ Charles R Greathouse IV, Jan 25 2012
(Magma) [17*n*(n+1): n in [0..50]]; // Vincenzo Librandi, Aug 20 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 16 2010
EXTENSIONS
Incorrect formulas and examples deleted by R. J. Mathar, Jan 04 2011
STATUS
approved