A019427 Continued fraction for tan(1/4).

0, 3, 1, 10, 1, 18, 1, 26, 1, 34, 1, 42, 1, 50, 1, 58, 1, 66, 1, 74, 1, 82, 1, 90, 1, 98, 1, 106, 1, 114, 1, 122, 1, 130, 1, 138, 1, 146, 1, 154, 1, 162, 1, 170, 1, 178, 1, 186, 1, 194, 1, 202, 1, 210, 1, 218, 1, 226, 1, 234, 1, 242, 1, 250, 1, 258, 1, 266, 1, 274, 1, 282, 1, 290, 1, 298, 1

Offset

0,2

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-4*(-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+4*x^2+x+3) / ((x-1)^2*(x+1)^2). (End)

Example

0.25534192122103626650448223... = 0 + 1/(3 + 1/(1 + 1/(10 + 1/(1 + ...)))). - Harry J. Smith, Jun 13 2009

Mathematica

 Join[{0, 3}, LinearRecurrence[{0, 2, 0, -1}, {1, 10, 1, 18}, 100]] (* Vincenzo Librandi, Jan 03 2016 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 91000); x=contfrac(tan(1/4)); for (n=0, 20000, write("b019427.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 13 2009
(PARI) Vec(x*(x^4-x^3+4*x^2+x+3)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013
(Magma) [0, 3] cat [(-1+3*(-1)^n-4*(-1+(-1)^n)*n)/2: n in [2..80]]; // Vincenzo Librandi, Jan 03 2016

Crossrefs

Cf. A161013 (decimal expansion). - Harry J. Smith, Jun 13 2009

Sequence in context: A127613 A211360 A178866 * A364850 A325830 A331155

Adjacent sequences: A019424 A019425 A019426 * A019428 A019429 A019430

Keyword

nonn,cofr,easy

Author

David W. Wilson

Status

approved