OFFSET
1,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: 6*x*(5 + 8*x - x^2)/(1-x)^3. - Bruno Berselli, Aug 27 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 12 2012
From Amiram Eldar, Mar 05 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(6))*Pi/sqrt(6))/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(6))*Pi/sqrt(6) - 1)/12. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {30, 138, 318}, 50] (* Vincenzo Librandi, Feb 12 2012 *)
PROG
(Magma) I:=[30, 138, 318]; [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 12 2012
(PARI) for(n=1, 40, print1(36*n^2-6", ")); \\ Vincenzo Librandi, Feb 12 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 19 2009
STATUS
approved