A130472 A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ).

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

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

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Lehman, F. Thomson Leighton, and Albert R. Meyer, Mathematics for Computer Science, Massachusetts Institute of Technology, 2015. See p. 210.

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/( (1-x)*(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

E.g.f.: (1/4)*(-exp(x) + (1-2*x)*exp(-x) ). - G. C. Greubel, Mar 31 2021

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 *)
(* Alternative: *)
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
(SageMath) [((-1)^n*(2*n+1) - 1)/4 for n in (0..70)] # G. C. Greubel, Mar 31 2021

Crossrefs

Sums of the form Sum_{k=0..n} k^p * q^k: A059841 (p=0,q=-1), this sequence (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

Cf. A001057, A038608.

Sequence in context: A168050 A001057 A127365 * A076938 A065033 A080513

Adjacent sequences: A130469 A130470 A130471 * A130473 A130474 A130475

Keyword

sign,easy,changed

Author

Clark Kimberling, May 28 2007

Status

approved