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URL: https://oeis.org/A143431

⇱ A143431 - OEIS


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A143431
Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, ...].
3
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
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).
EXAMPLE
1 - x + x^2 - x^3 - x^4 + x^5 - x^6 + x^7 + x^8 - x^9 + x^10 - x^11 + ...
MATHEMATICA
LinearRecurrence[{0, 0, 0, -1}, {1, -1, 1, -1}, 120] (* or *) PadRight[{}, 120, {1, -1, 1, -1, -1, 1, -1, 1}] (* Harvey P. Dale, Jul 15 2025 *)
PROG
(PARI) a(n) = (-1)^(n + n\4)
CROSSREFS
Convolution inverse of A143432.
Sequence in context: A112865 A114523 A130151 * A064179 A065357 A119665
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 14 2008
STATUS
approved