A143431 Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, ...].

1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1

Offset

0,1

Comments

Nonsimple continued fraction expansion of (1+sqrt 5)/2= A001622. - R. J. Mathar, Mar 08 2012

Links

Table of n, a(n) for n=0..101.

Formula

Euler transform of length 8 sequence [ -1, 1, 0, -2, 0, 0, 0, 1].

a(-1 - n) = a(n). a(n + 4) = - a(n).

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

a(n)=(1/4)*{-[(n+1) mod 8]+[(n+2) mod 8]-[(n+3) mod 8]+[(n+5) mod 8]-[(n+6) mod 8]+[(n+7) mod 8]}, with n>=0 [From Paolo P. Lava, Aug 25 2008]

Example

1 - x + x^2 - x^3 - x^4 + x^5 - x^6 + x^7 + x^8 - x^9 + x^10 - x^11 + ...

Prog

(PARI) a(n) = (-1)^(n + n\4)

Crossrefs

Convolution inverse of A143432.

Sequence in context: A112865 A114523 A130151 * A064179 A065357 A119665

Adjacent sequences: A143428 A143429 A143430 * A143432 A143433 A143434

Keyword

sign,easy

Author

Michael Somos, Aug 14 2008

Status

approved