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A075553
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Numerators in the Maclaurin series for arctan(1+x).
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5
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0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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Euler transform of length 8 sequence [ -1, 1, 1, -1, 0, -1, 0, 1]. - Michael Somos, Jul 16 2006
G.f.: x(1-x+x^2)/(1+x^4) = x(1-x)(1-x^4)(1-x^6)/((1-x^2)(1-x^3)(1-x^8)). a(-n) = a(n+4) = -a(n). - Michael Somos, Jul 16 2006
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MATHEMATICA
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a[n_] := I ((-1 - I)^n - (-1 + I)^n)/2^Floor[1 + n/2]; Table[a[n], {n, 0, 100}]
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PROG
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(PARI) a(n)=[0, 1, -1, 1, 0, -1, 1, -1][n%8+1] /* Michael Somos, Jul 16 2006 */
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CROSSREFS
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Cf. A075554.
Sequence in context: A341625 A166486 A046978 * A131729 A144609 A115517
Adjacent sequences: A075550 A075551 A075552 * A075554 A075555 A075556
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KEYWORD
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sign,easy
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AUTHOR
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Eric W. Weisstein, Sep 23 2002
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STATUS
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approved
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