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 A143431 Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, ...]. 3

%I #8 Apr 30 2014 01:37:11

%S 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,

%T -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,

%U -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

%N Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, ...].

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

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

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

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

%F 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]

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

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

%Y Convolution inverse of A143432.

%K sign,easy

%O 0,1

%A _Michael Somos_, Aug 14 2008

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Last modified December 5 00:23 EST 2023. Contains 367565 sequences. (Running on oeis4.)