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Search: id:A099842
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| A099842 |
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A transformation of x/(1-2x-2x^2). |
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+0
2
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| 1, -7, 45, -291, 1881, -12159, 78597, -508059, 3284145, -21229047, 137226717, -887047443, 5733964809, -37064931183, 239591481525, -1548743682699, 10011236540769, -64713650292711, 418315611378573, -2704034619149571, 17479154549033145, -112987031151647583
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The g.f. is the transform of the g.f. of A080953 under the mapping G(x)-> (-1/(1+x))G((x-1)/(x+1)). In general this mapping transforms x/(1-kx-kx^2) into (1-x)/(1+2(k+1)x-(2k-1)x^2).
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FORMULA
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G.f.: (1-x)/(1+6x-3x^2); a(n)=(1/2-sqrt(3)/3)(-3+2sqrt(3))^n+(1/2+sqrt(3)/3)(-3-2sqrt(3))^n; a(n)=(-1)^n*sum{k=0..n, binomial(n, k)(-1)^(n-k)*A080953(2k+2)/2}.
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CROSSREFS
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Adjacent sequences: A099839 A099840 A099841 this_sequence A099843 A099844 A099845
Sequence in context: A091127 A107125 A059937 this_sequence A115194 A062274 A143835
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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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