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A075553 Numerators in the Maclaurin series for arctan(1+x). 4
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 (list; graph; refs; listen; history; text; internal format)
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 */

CROSSREFS

Cf. A075554.

Sequence in context: A188260 A166486 A046978 * A131729 A144609 A115517

Adjacent sequences:  A075550 A075551 A075552 * A075554 A075555 A075556

KEYWORD

sign,easy

AUTHOR

Eric W. Weisstein, Sep 23 2002

STATUS

approved

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Last modified October 21 16:04 EDT 2019. Contains 328301 sequences. (Running on oeis4.)