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A019433 Continued fraction for tan(1/10). 5
0, 9, 1, 28, 1, 48, 1, 68, 1, 88, 1, 108, 1, 128, 1, 148, 1, 168, 1, 188, 1, 208, 1, 228, 1, 248, 1, 268, 1, 288, 1, 308, 1, 328, 1, 348, 1, 368, 1, 388, 1, 408, 1, 428, 1, 448, 1, 468, 1, 488, 1, 508, 1, 528, 1, 548, 1, 568, 1, 588, 1, 608, 1, 628, 1, 648, 1, 668, 1, 688, 1, 708, 1, 728 (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) = -1/2+(3*(-1)^n)/2+5*n-5*(-1)^n*n for n>1.

a(n) = 2*a(n-2)-a(n-4) for n>5.

G.f.: x*(x^4-x^3+10*x^2+x+9) / ((x-1)^2*(x+1)^2). (End)

EXAMPLE

0.10033467208545054505808004... = 0 + 1/(9 + 1/(1 + 1/(28 + 1/(1 + ...)))). - Harry J. Smith, Jun 14 2009

PROG

(PARI) { allocatemem(932245000); default(realprecision, 99000); x=contfrac(tan(1/10)); for (n=0, 20000, write("b019433.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 14 2009

(PARI) Vec(x*(x^4-x^3+10*x^2+x+9)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013

CROSSREFS

Cf. A161019 (decimal expansion). - Harry J. Smith, Jun 14 2009

Sequence in context: A202006 A195278 A092477 * A276634 A050312 A295575

Adjacent sequences:  A019430 A019431 A019432 * A019434 A019435 A019436

KEYWORD

nonn,cofr,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)