OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..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.: -(1 + 76*x + 79*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>=0} 1/a(n) = (coth(Pi/sqrt(78))*Pi/sqrt(78) + 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(78))*Pi/sqrt(78) + 1)/2. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 79, 313}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
78*Range[0, 40]^2+1 (* Harvey P. Dale, Dec 06 2018 *)
PROG
(Magma) I:=[1, 79, 313]; [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=0, 40, print1(78*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 21 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 26 2009
EXTENSIONS
Comment rewritten, a(0) added, and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved