A131730 a(4n) = n, a(4n+1) = -n-1, a(4n+2) = n+1, a(4n+3) = -n.

0, -1, 1, 0, 1, -2, 2, -1, 2, -3, 3, -2, 3, -4, 4, -3, 4, -5, 5, -4, 5, -6, 6, -5, 6, -7, 7, -6, 7, -8, 8, -7, 8, -9, 9, -8, 9, -10, 10, -9, 10, -11, 11, -10, 11, -12, 12, -11, 12, -13, 13, -12, 13, -14, 14, -13, 14, -15, 15, -14, 15, -16, 16, -15, 16, -17, 17, -16, 17, -18, 18, -17, 18, -19, 19, -18, 19, -20, 20, -19, 20, -21, 21, -20

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

From Wesley Ivan Hurt, May 29 2016: (Start)

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

a(n) + a(n-1) = a(n-4) + a(n-5) for n>4.

a(n) = (1+i^(2*n)-(1+3*i)*i^(-n)-(1-3*i)*i^n+2*n*i^(2n))/8 where i=sqrt(-1).

a(2k) = A110654(k), a(2k+1) = - A028242(k).

abs(a(-n-2)) = A246552(n). (End)

E.g.f.: (-3*sin(x) - cos(x) + x*sinh(x) - (x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 29 2016

a(n) = cos(n*Pi)*(2*n+1-2*cos(n*Pi/2)+cos(n*Pi)+6*sin(n*Pi/2))/8. - Wesley Ivan Hurt, Oct 01 2017

a(n) = (-1)^n*(n - 2*floor((n+1)/4) - floor((n+2)/4)). - Ridouane Oudra, Dec 10 2023

Maple

A131730:=n->(1+I^(2*n)-(1+3*I)*I^(-n)-(1-3*I)*I^n+2*n*I^(2*n))/8: seq(A131730(n), n=0..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Table[(1+I^(2n)-(1+3*I)*I^(-n)-(1-3*I)*I^n+2*n*I^(2 n))/8, {n, 0, 80}] (* Wesley Ivan Hurt, May 29 2016 *)
LinearRecurrence[{-1, 0, 0, 1, 1}, {0, -1, 1, 0, 1}, 50] (* G. C. Greubel, May 29 2016 *)

Crossrefs

Cf. A028242, A110654, A246552.

Sequence in context: A329400 A131909 A307319 * A029335 A029257 A194258

Adjacent sequences: A131727 A131728 A131729 * A131731 A131732 A131733

Keyword

sign,easy

Author

Paul Curtz, Sep 17 2007

Status

approved