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A099843
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A transform of the Fibonacci numbers.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| 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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MATHEMATICA
| CoefficientList[Series[(x - 1)/(x^2 - 4 x - 1), {x, 0, 30}], x] (* From Vladimir Joseph Stephan Orlovsky, June 10 2011 *)
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CROSSREFS
| Cf. A099842, A015448.
Sequence in context: A019992 A010917 A015448 * A035011 A113987 A188707
Adjacent sequences: A099840 A099841 A099842 * A099844 A099845 A099846
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 27 2004
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