A101676 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) with initial terms 1,0,-2,-1,0.

1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2, -1, 0, 0, 1, 0, -2

Offset

0,3

Comments

Partial sums of A101675. Partial sums are A101677.

Sequence has period 6. - Ralf Stephan, May 16 2007

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Formula

G.f.: (1 - x - x^2)/((1 - x)*(1 + x^2 + x^4)).

a(n) = -cos(2*Pi*n/3+Pi/3)/3 + sin(2*Pi*n/3+Pi/3)/sqrt(3) + 2*cos(Pi*n/3+Pi/6)/sqrt(3) - 1/3.

Mathematica

LinearRecurrence[{1, -1, 1, -1, 1}, {1, 0, -2, -1, 0}, 105] (* Ray Chandler, Sep 03 2015 *)

Prog

(PARI) x='x+O('x^100); Vec((1-x-x^2)/((1-x)*(1+x^2+x^4))) \\ G. C. Greubel, Sep 07 2018
(Magma) I:=[1, 0, -2, -1, 0]; [n le 5 select I[n] else Self(n-1) - Self(n-2) +Self(n-3) -Self(n-4) +Self(n-5): n in [1..100]]; // G. C. Greubel, Sep 07 2018

Crossrefs

Sequence in context: A352512 A364032 A333397 * A056560 A345415 A096608

Adjacent sequences: A101673 A101674 A101675 * A101677 A101678 A101679

Keyword

sign,easy

Author

Paul Barry, Dec 11 2004

Status

approved