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A330025
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a(n) = (-1)^floor(n/5) * sign(mod(n, 5)).
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1
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0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1
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OFFSET
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0,1
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COMMENTS
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This is a strong elliptic divisibility sequence t_n as given in [Kimberling, p. 16] where x = 1, y = 1, z = 1. - Michael Somos, Mar 17 2020
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LINKS
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FORMULA
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Euler transform of length 10 sequence [1, 0, 0, -1, -1, 0, 0, 0, 0, 1].
G.f.: x * (1 + x) * (1 + x^2) / (1 + x^5).
a(n) = (-1)^floor(n/5) * A011558(n) for all n in Z.
0 = a(n)*a(n+4) - a(n+1)*a(n+3) + a(n+2)^2) = a(n)*a(n+5) - a(n+1)*a(n+4) + a(n+2)*a(n+3) for all n in Z. - Michael Somos, Mar 17 2020
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EXAMPLE
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G.f. = x + x^2 + x^3 + x^4 - x^6 - x^7 - x^8 - x^9 + x^11 + x^12 + ...
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MATHEMATICA
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a[ n_] := (-1)^Quotient[n, 5] Sign@Mod[n, 5];
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PROG
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(PARI) {a(n) = (-1)^(n\5) * sign(n%5)};
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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