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A098178
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Expansion of (1+x)(1-x+x^2)/((1-x)(1+x^2)).
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6
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1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2
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OFFSET
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0,5
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COMMENTS
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Transform of A011782 under the Chebyshev mapping g(x)-> ((1-x^2)/(1+x^2)) * g(x/(1+x^2)).
Multiplicative with a(2) = 0, a(2^e) = 2 if e >= 2, a(p^e) = 1. [David W. Wilson, Jun 12 2005]
1, followed by period 4, repeat [1, 0, 1, 2]. [Joerg Arndt, Jan 06 2014]
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LINKS
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FORMULA
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G.f.: (1+x)(1-x+x^2)/((1-x)(1+x^2)).
a(n) = 1 + cos(Pi*n/2) - 0^n.
a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1+x)(1-x+x^2)/((1-x)(1+x^2)), {x, 0, 120}], x] (* or *) PadRight[{1}, 120, {2, 1, 0, 1}] (* Harvey P. Dale, May 01 2013 *)
Table[Sign[n] - 1 + Sqrt[Mod[(n - 2)^2, 8]], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 04 2014 *)
Join[{1}, LinearRecurrence[{1, -1, 1}, {1, 0, 1}, 104]] (* Ray Chandler, Sep 03 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn,mult
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AUTHOR
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STATUS
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approved
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