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 A099917 Expansion of (1+x^2)^2/(1+x^3+x^6). 1
 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0, 2, -1, 1, -2, 0, -1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The denominator is the 9th cyclotomic polynomial. The g.f. is a Chebyshev transform of that of (-1)^n*A052931(n) by the Chebyshev mapping g(x)->(1/(1+x^2))g(x/(1+x^2)). The reciprocal of the 9th cyclotomic polynomial A014018 is given by sum{k=0..n, A099917(n-k)(k/2+1)(-1)^(k/2)(1+(-1)^k)/2}. LINKS Table of n, a(n) for n=0..100. FORMULA a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(j, n-2k-2j)3^k(-1/3)^(n-2k)}}; a(n)=sum{k=0..n, A014018(n-k)C(2, k/2)(1+(-1)^k)/2}. CROSSREFS Cf. A099916. Sequence in context: A060575 A236074 A099916 * A137412 A355913 A025925 Adjacent sequences: A099914 A099915 A099916 * A099918 A099919 A099920 KEYWORD easy,sign AUTHOR Paul Barry, Oct 30 2004 STATUS approved

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Last modified September 23 21:37 EDT 2023. Contains 365554 sequences. (Running on oeis4.)