OFFSET
0,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Vincenzo Librandi, Jul 08 2012: (Start)
G.f.: (1 - 50*x - 47*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 19 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)) - 1)/2. (End)
MATHEMATICA
CoefficientList[Series[(1-50*x-47*x^2)/(x-1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3, -3, 1}, {-1, 47, 191}, 40] (* Harvey P. Dale, Dec 13 2017 *)
PROG
(PARI) A065532(n)=48*n^2-1
(PARI) { for (n=0, 1000, write("b065532.txt", n, " ", 48*n^2 - 1) ) } \\ Harry J. Smith, Oct 21 2009
(Magma) [48*n^2 - 1: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Labos Elemer, Nov 28 2001
EXTENSIONS
Better description from Randall L Rathbun, Jan 19 2002
Offset changed from 1 to 0 by Harry J. Smith, Oct 21 2009
STATUS
approved