OFFSET
0,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: 12*(1 + 10*x + 13*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 06 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/(2*sqrt(3)))*Pi/(2*sqrt(3)) + 1)/24.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/(2*sqrt(3)))*Pi/(2*sqrt(3)) + 1)/24. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {12, 156, 588}, 50] (* Vincenzo Librandi, Feb 14 2012 *)
PROG
(Magma) I:=[12, 156, 588]; [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(144*n^2 + 12", ")); \\ 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