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Search: id:A099843
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| A099843 |
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A transform of the Fibonacci numbers. |
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+0
1
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| 1, -5, 21, -89, 377, -1597, 6765, -28657, 121393, -514229, 2178309, -9227465, 39088169, -165580141, 701408733, -2971215073, 12586269025, -53316291173, 225851433717, -956722026041, 4052739537881, -17167680177565, 72723460248141, -308061521170129, 1304969544928657
(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 A000045 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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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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G.f.: (1-x)/(1+4x-x^2); a(n)=(sqrt(5)-2)^n(1/2-3sqrt(5)/10)+(-sqrt(5)-2)^n(1/2+3sqrt(5)/10); a(n)=(-1)^nFib(3n+2).
a(n)=-4*a(n-1)+a(n-2), a(0)=1, a(1)=-5. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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CROSSREFS
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Cf. A099842, A015448.
Sequence in context: A019992 A010917 A015448 this_sequence A035011 A113987 A125784
Adjacent sequences: A099840 A099841 A099842 this_sequence A099844 A099845 A099846
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KEYWORD
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easy,sign,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 27 2004
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