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A019428 Continued fraction for tan(1/5). 3
0, 4, 1, 13, 1, 23, 1, 33, 1, 43, 1, 53, 1, 63, 1, 73, 1, 83, 1, 93, 1, 103, 1, 113, 1, 123, 1, 133, 1, 143, 1, 153, 1, 163, 1, 173, 1, 183, 1, 193, 1, 203, 1, 213, 1, 223, 1, 233, 1, 243, 1, 253, 1, 263, 1, 273, 1, 283, 1, 293, 1, 303, 1, 313, 1, 323, 1, 333, 1, 343, 1, 353, 1, 363, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,20000

G. Xiao, Contfrac

Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

a(n) = (-1+3*(-1)^n-5*(-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+5*x^2+x+4) / ((x-1)^2*(x+1)^2). - Colin Barker, Sep 08 2013

EXAMPLE

0.20271003550867248332135827... = 0 + 1/(4 + 1/(1 + 1/(13 + 1/(1 + ...)))) [From Harry J. Smith, Jun 13 2009]

PROG

(PARI) { allocatemem(932245000); default(realprecision, 93000); x=contfrac(tan(1/5)); for (n=0, 20000, write("b019428.txt", n, " ", x[n+1])); } [From Harry J. Smith, Jun 13 2009]

(PARI) Vec(x*(x^4-x^3+5*x^2+x+4)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013

CROSSREFS

Cf. A161014 Decimal expansion. [From Harry J. Smith, Jun 13 2009]

Sequence in context: A157404 A135704 A002564 * A184753 A055252 A193956

Adjacent sequences:  A019425 A019426 A019427 * A019429 A019430 A019431

KEYWORD

nonn,cofr,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 18 04:30 EST 2014. Contains 252079 sequences.