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Search: id:A115602
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| A115602 |
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a(n) = denominator of b(n), where b(1) = 1, b(n+1) = sum{k=1 to n} b(k)^((-1)^(n-k+1)). |
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4
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| 1, 1, 1, 2, 5, 22, 115, 1034, 10925, 197494, 4184275, 151477898, 6422862125, 465188624758, 39455642033875, 5715772632401546, 42157495781846875, 12214606115442103802, 4144208307842893353125, 2401477064538725702199814
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Sequence of numerators does not match sequence of denominators.
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FORMULA
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a(n) = c(n-2)/GCD(c(n-1),c(n-2)), where c(n) = product{k=1 to floor(n/2)} (3*2^(n-2k) -1).
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EXAMPLE
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{b(n)} begins 1, 1, 2, 5/2, 22/5, 115/22, 1034/115,...
So b(7) = 1 + 1 + 1/2 + 5/2 + 5/22 + 115/22 + 115/1034 = 10925/1034, and therefore a(7) = 1034.
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MATHEMATICA
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b = {1}; Do[AppendTo[b, Sum[b[[k]]^((-1)^(n - k + 1)), {k, 1, n}]], {n, 1, 30}]; Table[Denominator[b[[j]]], {j, 1, Length[b]}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 16 2007
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CROSSREFS
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Cf. A115587, A115600, A115601.
Sequence in context: A126797 A101206 A041807 this_sequence A115601 A015557 A066305
Adjacent sequences: A115599 A115600 A115601 this_sequence A115603 A115604 A115605
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 13 2006
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 16 2007
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