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A163812
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Expansion of (1 - x^5) * (1 - x^6) / ((1 - x) * (1 - x^10)) in powers of x.
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4
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1, 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, -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
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OFFSET
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0,1
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LINKS
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FORMULA
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Euler transform of length 10 sequence [ 1, 0, 0, 0, -1, -1, 0, 0, 0, 1].
a(5*n) = 0 unless n=0.
a(n) = -a(-n) unless n=0. a(n+5) = -a(n) unless n=0 or n=-5.
G.f.: (1 + x^2 + x^4) / (1 - x + x^2 - x^3 + x^4).
G.f.: A(x) = 1 / (1 - x / ( 1 + x^4 / (1 + x^2))) = 1 + x / (1 - x / (1 + x^3 / (1 + x^2 / (1 + x / (1 - x))))). - Michael Somos, Jan 03 2013
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EXAMPLE
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G.f. = 1 + x + x^2 + x^3 + x^4 - x^6 - x^7 - x^8 - x^9 + x^11 + x^12 + x^13 + ...
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MATHEMATICA
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a[ n_] := Boole[n == 0] + (-1)^Quotient[n, 5] Sign@Mod[n, 5]; (* Michael Somos, Jun 17 2015 *)
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PROG
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(PARI) {a(n) = (n==0) + [0, 1, 1, 1, 1, 0, -1, -1, -1, -1][n%10 + 1]};
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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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