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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 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-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). (End) EXAMPLE 0.20271003550867248332135827... = 0 + 1/(4 + 1/(1 + 1/(13 + 1/(1 + ...)))). - Harry J. Smith, Jun 13 2009 MATHEMATICA Join[{0, 4}, LinearRecurrence[{0, 2, 0, -1}, {1, 13, 1, 23}, 100]] (* Vincenzo Librandi, Jan 03 2016 *) PROG (PARI) { allocatemem(932245000); default(realprecision, 93000); x=contfrac(tan(1/5)); for (n=0, 20000, write("b019428.txt", n, " ", x[n+1])); } \\ 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 (MAGMA) [0, 4] cat [(-1+3*(-1)^n-5*(-1+(-1)^n)*n)/2: n in [2..80]]; // Vincenzo Librandi, Jan 03 2016 CROSSREFS Cf. A161014 (decimal expansion). - Harry J. Smith, Jun 13 2009 Sequence in context: A002564 A287640 A322078 * A303547 A184753 A324186 Adjacent sequences:  A019425 A019426 A019427 * A019429 A019430 A019431 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)