OFFSET
1,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(-75 - 78*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 23 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(2*sqrt(19)))*Pi/(2*sqrt(19)))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(19)))*Pi/(2*sqrt(19)) - 1)/2. (End)
MATHEMATICA
76*Range[40]^2-1 (* or *) LinearRecurrence[{3, -3, 1}, {75, 303, 683}, 40] (* Harvey P. Dale, Jan 18 2012 *)
PROG
(Magma) I:=[75, 303, 683]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 21 2012
(PARI) for(n=1, 40, print1(76*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 21 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 26 2009
EXTENSIONS
Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved