OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Leo Tavares, Illustration: Stellar Stars
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1 + 22*x + 25*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 02 2023: (Start)
Sum_{n>=0} 1/a(n) = 1/2 + coth(Pi/(2*sqrt(6))*Pi/(4*sqrt(6)).
Sum_{n>=0} (-1)^n/a(n) = 1/2 + cosech(Pi/(2*sqrt(6)))*Pi/(4*sqrt(6)). (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 25, 97}, 50] (* Vincenzo Librandi, Feb 14 2012 *)
PROG
(Magma) I:=[1, 25, 97]; [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 14 2012
(PARI) for(n=0, 40, print1(24*n^2+1", ")); \\ Vincenzo Librandi, Feb 14 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 21 2009
EXTENSIONS
Comment rewritten, a(0) added by R. J. Mathar, Oct 16 2009
STATUS
approved