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A099494 A Chebyshev transform of Fib(n)+(-1)^n. 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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

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

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

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-2k)+(-1)^(n-2k)}; a(n)=A014019(n-1)+A000484(n).

CROSSREFS

Sequence in context: A282714 A280634 A281491 * A030341 A258832 A121444

Adjacent sequences:  A099491 A099492 A099493 * A099495 A099496 A099497

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 19 2004

STATUS

approved

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Last modified May 14 09:58 EDT 2021. Contains 343879 sequences. (Running on oeis4.)