A019430 Continued fraction for tan(1/7).

0, 6, 1, 19, 1, 33, 1, 47, 1, 61, 1, 75, 1, 89, 1, 103, 1, 117, 1, 131, 1, 145, 1, 159, 1, 173, 1, 187, 1, 201, 1, 215, 1, 229, 1, 243, 1, 257, 1, 271, 1, 285, 1, 299, 1, 313, 1, 327, 1, 341, 1, 355, 1, 369, 1, 383, 1, 397, 1, 411, 1, 425, 1, 439, 1, 453, 1, 467, 1, 481, 1, 495, 1, 509, 1

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• cofr
• easy

Examples

			0.14383695943619093528003059... = 0 + 1/(6 + 1/(1 + 1/(19 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 14 2009
		

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).

Crossrefs

Cf. A161016 (decimal expansion), A019425 through A019433.

Programs

Magma

[0, 6] cat [(-1+3*(-1)^n-7*(-1+(-1)^n)*n)/2: n in [2..80]]; // Vincenzo Librandi, Jan 03 2016

Mathematica

Block[{$MaxExtraPrecision=1000},ContinuedFraction[Tan[1/7],80]] (* Harvey P. Dale, Feb 01 2013 *)
Join[{0, 6}, LinearRecurrence[{0, 2, 0, -1}, {1, 19, 1, 33}, 100]] (* Vincenzo Librandi, Jan 03 2016 *)

PARI

{ allocatemem(932245000); default(realprecision, 96000); x=contfrac(tan(1/7)); for (n=0, 20000, write("b019430.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 14 2009

PARI

Vec(x*(x^4-x^3+7*x^2+x+6)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013

Formula

From Colin Barker, Sep 08 2013: (Start)

a(n) = (-1+3*(-1)^n-7*(-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+7*x^2+x+6) / ((x-1)^2*(x+1)^2). (End)