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A112030 a(n) = (2 + (-1)^n) * (-1)^floor(n/2). 12
3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = A010684(n+1) * (-1)^floor(n/2);

the fractions A112031(n)/A112032(n) give the partial sums of a(n)/floor((n+4)/2).

Sum of the two Cartesian coordinates from the image of the point (2,1) after n 90-degree counterclockwise rotations about the origin. - Wesley Ivan Hurt, Jul 06 2013

LINKS

Table of n, a(n) for n=0..77.

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

FORMULA

O.g.f.: (3+x)/(1+x^2). - R. J. Mathar, Jan 09 2008

MAPLE

A112030 := proc(n)

        (2 + (-1)^n) * (-1)^floor(n/2) ;

end proc: # R. J. Mathar, Jul 09 2013

PROG

(PARI) a(n)=[3, 1, -3, -1][n%4+1] \\ Charles R Greathouse IV, Aug 21 2011

CROSSREFS

Cf. A016116, A112033.

Sequence in context: A063062 A066056 A153284 * A010684 A176040 A125768

Adjacent sequences:  A112027 A112028 A112029 * A112031 A112032 A112033

KEYWORD

sign,easy

AUTHOR

Reinhard Zumkeller, Aug 27 2005

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)