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Search: id:A114014
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| A114014 |
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A series expansion of a quadric Jasinski rational polynomial based on A112627 that is Farey like in p[1/2]=1. |
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+0
1
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| 1, 7, 33, 127, 529, 2031, 8465, 32495, 135441, 519919, 2167057, 8318703, 34672913, 133099247, 554766609, 2129587951, 8876265745, 34073407215, 142020251921, 545174515439, 2272324030737, 8722792247023, 36357184491793
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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if p[x]=k*Product[(x-a(i),{i,1,n}]/Product[(x-b(i),{i,1,n}] and a(i), b(i) and k are real and rational, then p[x] will be rational. If you keep the roots out of the interior of the interval (0,1), then Farey function on that interval will be relatively smooth as well. In this case the 1/4 root makes that impossible but adding an x for a zero roots ties down the zero end and the other end is at 2.
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FORMULA
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b(n) = coefficients of (9/64)*(x + 1/2)^4/(x*(x - 1/4)*(x + 1/4)*(x + 1)); a(n) = 2*a(n-1) + 3; generating function = 1/(exp(x)-1).
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MATHEMATICA
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b = Delete[ -(64/9)*ReplacePart[Table[Coefficient[Series[(9/64)*(x + 1/2)^4/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, -1, 30}], -9/64, 2], 1]
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CROSSREFS
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Cf. A112627.
Sequence in context: A131211 A100855 A000605 this_sequence A066810 A034577 A141291
Adjacent sequences: A114011 A114012 A114013 this_sequence A114015 A114016 A114017
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2006
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