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.: 29*x*(-28-31*x+x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 20 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(29))*Pi/sqrt(29))/58.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(29))*Pi/sqrt(29) - 1)/58. (End)
MAPLE
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {812, 3335, 7540}, 40] (* or *) 29 (29 Range[40]^2 - 1) (* Harvey P. Dale, Oct 31 2011 *)
PROG
(Magma) I:=[812, 3335, 7540]; [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 18 2012
(PARI) for(n=1, 40, print1(841*n^2-29", ")); \\ Vincenzo Librandi, Feb 18 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 24 2009
EXTENSIONS
Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
STATUS
approved