A105367 Expansion of (1-x^3)/(1-x^5).

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

Offset

0,1

Comments

Periodic {1,0,0,-1,0}. Partial sums of A105368. Binomial transform of A105370.

Links

Table of n, a(n) for n=0..86.

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

Formula

G.f.: (1+x+x^2)/(1+x+x^2+x^3+x^4);

a(n) = sqrt(2/5 - 2*sqrt(5)/25)*cos(4*Pi*n/5 + 3*Pi/10) + sqrt(2/5 + 2*sqrt(5)/25)*sin(2*Pi*n/5 + 2*Pi/5).

Crossrefs

Sequence in context: A244612 A262805 A213728 * A232990 A285076 A338353

Adjacent sequences: A105364 A105365 A105366 * A105368 A105369 A105370

Keyword

easy,sign

Author

Paul Barry, Apr 01 2005

Status

approved