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A100261 Continued fraction expansion of cot(1-Pi/4). 2
4, 1, 1, 2, 2, 1, 16, 1, 4, 2, 5, 1, 28, 1, 7, 2, 8, 1, 40, 1, 10, 2, 11, 1, 52, 1, 13, 2, 14, 1, 64, 1, 16, 2, 17, 1, 76, 1, 19, 2, 20, 1, 88, 1, 22, 2, 23, 1, 100, 1, 25, 2, 26, 1, 112, 1, 28, 2, 29, 1, 124, 1, 31, 2, 32, 1, 136, 1, 34, 2, 35, 1, 148, 1, 37, 2, 38, 1, 160, 1, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Lipshitz, Leonard, and A. van der Poorten. "Rational functions, diagonals, automata and arithmetic." In Number Theory, Richard A. Mollin, ed., Walter de Gruyter, Berlin (1990): 339-358.

LINKS

Table of n, a(n) for n=1..81.

A. J. van der Poorten, Continued fraction expansions of values of the exponential function...

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

FORMULA

This number is also -Im[ (e^(2i)+i)/(e^(2i)-i) ].

Periodic part is ...2, 3k+2, 1, 12k+16, 1, 3k+4, ... (k=0..inf).

G.f.: -x*(x^11-x^10+2*x^9-2*x^8+x^7-8*x^6-x^5-2*x^4-2*x^3-x^2-x-4) / ((x-1)^2*(x+1)^2*(x^2-x+1)^2*(x^2+x+1)^2). - Colin Barker, Jul 15 2013

EXAMPLE

4.588037824983899981397906503733748769677138839382189177607356840...

MATHEMATICA

ContinuedFraction[ -Im[(E^(2I) + I)/(E^(2I) - I)], 80] (* Robert G. Wilson v, Nov 20 2004 *)

CROSSREFS

Cf. A005131.

Sequence in context: A112985 A293769 A073693 * A016526 A247341 A030747

Adjacent sequences:  A100258 A100259 A100260 * A100262 A100263 A100264

KEYWORD

nonn,cofr,easy

AUTHOR

Ralf Stephan, Nov 18 2004

STATUS

approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)