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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 A025925 A240857

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 October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)