OFFSET
0,1
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.: 17*(1 + 15*x + 18*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 14 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(17))*Pi/sqrt(17) + 1)/34.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(17))*Pi/sqrt(17) + 1)/34. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {17, 306, 1173}, 50] (* Vincenzo Librandi, Feb 15 2012 *)
289*Range[0, 40]^2+17 (* Harvey P. Dale, Dec 26 2019 *)
PROG
(Magma) I:=[17, 306, 1173]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2012
(PARI) for(n=0, 50, print1(289*n^2 + 17", ")); \\ Vincenzo Librandi, Feb 15 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 22 2009
EXTENSIONS
Comment rewritten, a(0) added by R. J. Mathar, Oct 16 2009
STATUS
approved