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A143431
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Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, ...].
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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 (paoloplava(AT)gmail.com), Aug 25 2008]
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EXAMPLE
| 1 - x + x^2 - x^3 - x^4 + x^5 - x^6 + x^7 + x^8 - x^9 + x^10 - x^11 + ...
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PROG
| (PARI) {a(n) = (-1)^(n + n \ 4)}
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CROSSREFS
| Convolution inverse of A143432.
Sequence in context: A112865 A114523 A130151 * A064179 A065357 A121241
Adjacent sequences: A143428 A143429 A143430 * A143432 A143433 A143434
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 14 2008
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