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.: 14*x*(13 + 16*x - x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 09 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(14))*Pi/sqrt(14))/28.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(14))*Pi/sqrt(14) - 1)/28. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {182, 770, 1750}, 40] (* Vincenzo Librandi, Feb 14 2012 *)
196*Range[40]^2-14 (* Harvey P. Dale, Oct 11 2023 *)
PROG
(Magma) I:=[182, 770, 1750]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(196*n^2 - 14", ")); \\ Vincenzo Librandi, Feb 14 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 21 2009
EXTENSIONS
Comment rewritten by R. J. Mathar, Oct 16 2009
STATUS
approved