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A100261
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Continued fraction expansion of cot(1-Pi/4).
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3
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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
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
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FORMULA
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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..oo).
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
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EXAMPLE
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4.588037824983899981397906503733748769677138839382189177607356840...
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MATHEMATICA
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ContinuedFraction[ -Im[(E^(2I) + I)/(E^(2I) - I)], 80] (* Robert G. Wilson v, Nov 20 2004 *)
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PROG
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(PARI) A100261(n) = if(1==n, 4, if(n<4, 1, n=n-4; my(k=n\6); if(!(n%6), 2, if(1==(n%6), 3*k + 2, if(3==(n%6), 12*k + 16, if(5==(n%6), 3*k + 4, 1)))))); \\ Antti Karttunen, Feb 15 2023
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CROSSREFS
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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STATUS
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approved
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