A112030 - OEIS

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A112030

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

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

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

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

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

MATHEMATICA

LinearRecurrence[{0, -1}, {3, 1}, 100] (* Jean-François Alcover, Nov 24 2020 *)