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Search: id:A099837
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| A099837 |
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Expansion of (1-x^2)/(1+x+x^2). |
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+0
10
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| 1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A transform of (-1)^n.
Row sums of Riordan array ((1-x)/(1+x),x/(1+x)^2), A110162.
Let b(n)=sum{k=0..floor(n/2), binomial(n-k,k)(-1)^(n-2k)}. Then a(n)=b(n)-b(n-2)=A049347(n)-A049347(n-2) (n>0). The g.f. 1/(1+x) of (-1)^n is transformed to (1-x^2)/(1+x+x^2) under the mapping G(x)->((1-x^2)/(1+x^2))G(x/(1+x^2)). Partial sums of A099838.
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FORMULA
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G.f.: (1-x^2)/(1+x+x^2); a(n)=sum{j=0..n, (C(1, j/2)(-1)^(j/2)(1+(-1)^j)/2)*sum{k=0..floor((n-j)/2), C(n-j-k, k)(-1)^(n-j-k)}}; a(n)=2cos(2*pi*n/3)-0^n.
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CROSSREFS
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Cf. A100051, A100063.
Cf. A061347, A098554.
Sequence in context: A015182 A057559 A016010 this_sequence A100051 A122876 A100063
Adjacent sequences: A099834 A099835 A099836 this_sequence A099838 A099839 A099840
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 27 2004
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