OFFSET
0,2
COMMENTS
The odd-indexed terms from and after a(3) are equal to 18n+7. - Harvey P. Dale, Sep 26 2021
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
From Colin Barker, Sep 08 2013: (Start)
a(n) = (-1+3*(-1)^n-9*(-1+(-1)^n)*n)/2 for n>1.
a(n) = 2*a(n-2)-a(n-4) for n>5.
G.f.: x*(x^4-x^3+9*x^2+x+8) / ((x-1)^2*(x+1)^2). (End)
EXAMPLE
0.11157062783380058372650480... = 0 + 1/(8 + 1/(1 + 1/(25 + 1/(1 + ...)))). - Harry J. Smith, Jun 14 2009
MATHEMATICA
Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Tan[1/9], 100]] (* or *) LinearRecurrence[{0, 2, 0, -1}, {0, 8, 1, 25, 1, 43}, 80] (* Harvey P. Dale, Sep 26 2021 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 98000); x=contfrac(tan(1/9)); for (n=0, 20000, write("b019432.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 14 2009
(PARI) Vec(x*(x^4-x^3+9*x^2+x+8)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013
CROSSREFS
KEYWORD
nonn,cofr,easy
AUTHOR
STATUS
approved