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URL: https://oeis.org/A019431

⇱ A019431 - OEIS

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A019431
Continued fraction for tan(1/8).
3
0, 7, 1, 22, 1, 38, 1, 54, 1, 70, 1, 86, 1, 102, 1, 118, 1, 134, 1, 150, 1, 166, 1, 182, 1, 198, 1, 214, 1, 230, 1, 246, 1, 262, 1, 278, 1, 294, 1, 310, 1, 326, 1, 342, 1, 358, 1, 374, 1, 390, 1, 406, 1, 422, 1, 438, 1, 454, 1, 470, 1, 486, 1, 502, 1, 518, 1, 534, 1, 550, 1, 566, 1, 582
OFFSET
0,2
FORMULA
From Colin Barker, Sep 08 2013: (Start)
a(n) = (-1+3*(-1)^n-8*(-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+8*x^2+x+7) / ((x-1)^2*(x+1)^2). (End)
EXAMPLE
0.12565513657513096779267821... = 0 + 1/(7 + 1/(1 + 1/(22 + 1/(1 + ...)))). - Harry J. Smith, Jun 14 2009
MATHEMATICA
Join[{0, 7}, LinearRecurrence[{0, 2, 0, -1}, {1, 22, 1, 38}, 100]] (* Vincenzo Librandi, Jan 03 2016 *)
Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Tan[1/8], 100]] (* Harvey P. Dale, Jul 14 2025 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 97000); x=contfrac(tan(1/8)); for (n=0, 20000, write("b019431.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 14 2009
(PARI) Vec(x*(x^4-x^3+8*x^2+x+7)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013
(Magma) [0, 7] cat [(-1+3*(-1)^n-8*(-1+(-1)^n)*n)/2: n in [2..80]]; // Vincenzo Librandi, Jan 03 2016
CROSSREFS
Cf. A161017 (decimal expansion), A019425 through A019433.
Sequence in context: A390604 A050310 A178445 * A264615 A261248 A214686
KEYWORD
nonn,cofr,easy
STATUS
approved