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
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f: 6*x*(7+4*x+x^2)/(1-x)^3.
From Amiram Eldar, Mar 05 2023: (Start)
Sum_{n>=1} 1/a(n) = (coth(Pi/sqrt(6))*Pi/sqrt(6) - 1)/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = (1 - cosech(Pi/sqrt(6))*Pi/sqrt(6))/12. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {42, 150, 330}, 40]
PROG
(Magma) I:=[42, 150, 330]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];
(PARI) a(n)=36*n^2+6 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 20 2009
STATUS
approved