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A130472 A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ). 15
0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10, -11, 11, -12, 12, -13, 13, -14, 14, -15, 15, -16, 16, -17, 17, -18, 18, -19, 19, -20, 20, -21, 21, -22, 22, -23, 23, -24, 24, -25, 25, -26, 26, -27, 27, -28, 28, -29, 29, -30, 30, -31, 31, -32, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Pisano period lengths:  1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, ... - R. J. Mathar, Aug 10 2012

Partial sums of A038608. - Stanislav Sykora, Nov 27 2013

LINKS

Table of n, a(n) for n=0..64.

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

Index entries for sequences that are permutations of the integers

FORMULA

a(n) = -A001057(n).

a(2n) = n, a(2n+1)=-n-1.

a(n) = Sum_{k=0..n} k*(-1)^k.

a(n) = -a(n-1) +a(n-2) +a(n-3).

G.f.: x / ((x-1)*(1+x)^2). - R. J. Mathar, Feb 20 2011

a(n) = floor( (n/2)*(-1)^n ). - Wesley Ivan Hurt, Jun 14 2013

a(n) = ceiling( n/2 )*(-1)^n. - Wesley Ivan Hurt, Oct 22 2013

a(n) = ((-1)^n*(2*n+1)-1)/4. - Adriano Caroli, Mar 28 2015

MAPLE

A130472:=n->ceil(n/2)*(-1)^n; seq(A130472(k), k=0..50); # Wesley Ivan Hurt, Oct 22 2013

MATHEMATICA

CoefficientList[Series[(x^2 - x)/(1 - x^2)^2, {x, 0, 64}], x] (* Geoffrey Critzer, Sep 29 2013 *)

LinearRecurrence[{-1, 1, 1}, {0, -1, 1}, 70] (* Harvey P. Dale, Mar 02 2018 *)

PROG

(MAGMA) [((-1)^n*(2*n+1)-1)/4: n in [0..80]]; // Vincenzo Librandi, Mar 29 2015

(PARI) a(n)=(-1)^n*n\2 \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Cf. A001057, A038608.

Sequence in context: A168050 A065033 A001057 * A076938 A080513 A004526

Adjacent sequences:  A130469 A130470 A130471 * A130473 A130474 A130475

KEYWORD

sign,easy

AUTHOR

Clark Kimberling, May 28 2007

STATUS

approved

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Last modified May 25 12:47 EDT 2018. Contains 304562 sequences. (Running on oeis4.)