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A075553

Numerators in the Maclaurin series for arctan(1+x).

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

0,1

LINKS

Table of n, a(n) for n=0..104.

FORMULA

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

MATHEMATICA

a[n_] := I ((-1 - I)^n - (-1 + I)^n)/2^Floor[1 + n/2]; Table[a[n], {n, 0, 100}]

PROG

(PARI) a(n)=[0, 1, -1, 1, 0, -1, 1, -1][n%8+1] /* Michael Somos, Jul 16 2006 */