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A134967 List of quadruples: [-2n-1, 2n+2, -2n-1, 2n+2]. 6
-1, 2, -1, 2, -3, 4, -3, 4, -5, 6, -5, 6, -7, 8, -7, 8, -9, 10, -9, 10, -11, 12, -11, 12, -13, 14, -13, 14, -15, 16, -15, 16, -17, 18, -17, 18, -19, 20, -19, 20, -21, 22, -21, 22, -23, 24, -23, 24, -25, 26, -25, 26, -27, 28, -27, 28, -29, 30, -29, 30, -31, 32, -31, 32, -33, 34, -33, 34, -35, 36, -35, 36, -37, 38, -37, 38, -39 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences are 3, -3, 3, -5, 7, -7, 7, -9, 11, -11, 11, ... .

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = (1-(2*n+3)*(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/4. - Luce ETIENNE, Sep 04 2016

a(n) = cos((n-1)*Pi)*(2*n+3+2*cos(n*Pi/2)-cos(n*Pi)+2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 02 2017

From Colin Barker, Oct 05 2017: (Start)

G.f.: -(1 - x - x^2 - x^3) / ((1 - x)*(1 + x)^2*(1 + x^2)).

a(n) = (1 - 3*(-1)^n - (1-i)*(-i)^n - (1+i)*i^n - 2*(-1)^n*n) / 4 were i=sqrt(-1).

(End)

MATHEMATICA

Flatten[Table[{-2n-1, 2n+2, -2n-1, 2n+2}, {n, 0, 20}]] (* Harvey P. Dale, Oct 19 2011 *)

PROG

(MAGMA) [(1-(2*n+3)*(-1)^n-2*(-1)^((2*n+1-(-1)^n)div 4))/4: n in [0..80]]; /* or * / &cat [[-2*n-1, 2*n+2, -2*n-1, 2*n+2]: n in [0..30]]; // Vincenzo Librandi, Oct 04 2017

(PARI) Vec(-(1 - x - x^2 - x^3) / ((1 - x)*(1 + x)^2*(1 + x^2)) + O(x^100)) \\ Colin Barker, Oct 05 2017

CROSSREFS

Sequence in context: A059261 A285869 A162330 * A320581 A240855 A084612

Adjacent sequences:  A134964 A134965 A134966 * A134968 A134969 A134970

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Feb 04 2008

STATUS

approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)