A099494 A Chebyshev transform of Fibonacci(n)+(-1)^n.

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

Offset: 0

Author

Paul Barry, Oct 19 2004

Keywords

• easy
• sign

Comments

A Chebyshev transform of A008346, which has g.f. 1/(1-2x^2-x^3). The image of G(x) under the Chebyshev transform is (1/(1+x^2))*G(x/(1+x^2)).

Periodic with period length 30. - Ray Chandler, Sep 08 2015

Links

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

Crossrefs

Cf. A000484, A008346, A014019

Formula

G.f.: (1+x^2)^2/(1+x^2-x^3+x^4+x^6).

a(n) = -a(n-2)+a(n-3)-a(n-4)-a(n-6).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*(F(n-2*k)+(-1)^(n-2*k)).

a(n) = A014019(n-1) + A000484(n).