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	`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 April 1 03:55 EDT 2020. Contains 333155 sequences. (Running on oeis4.)