id:A099917 - OEIS Search Results

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Expansion of (1+x^2)^2/(1+x^3+x^6).

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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; listen)

	OFFSET	`0,3`
	COMMENT	`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}.`
	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: A057554 A060575 A099916 this_sequence A137412 A025925 A109066` `Adjacent sequences: A099914 A099915 A099916 this_sequence A099918 A099919 A099920`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 30 2004`

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Last modified July 24 12:00 EDT 2008. Contains 142294 sequences.

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