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Search: id:A117465
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| A117465 |
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Denominators of f(n), n=1...inf(integers) for a function to analyze paths to stable orbits of the logistic equation. |
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1
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| 9, 0, 15, 0, 105, 24, 945, 120, 3465, 360, 9009, 840, 19305, 1680, 36465, 3024, 62985, 5040, 101745, 7920, 156009, 11880, 229425, 17160, 326025, 24024, 450225, 32760, 606825, 43680, 801009, 57120
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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I came up with the equation to help analyze the path to stable orbits of the logistic function f(n+1) = k*n(1-n) for f(n) with n => 9, then f(n)*A072346(n-5) = A072346(n+3) where A072346 is "Volume of n-dimensional sphere of radius r...;sequence gives denominator of C_n." The even numbers n correspond to A052762 "A simple grammar product of 4 consecutive integers". For f(n) the numerator for even n is -1 and for odd n is -16
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FORMULA
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f(n) := n -> (1/((n/4)+(n^2/4)-(n^3/16)-1))/n
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EXAMPLE
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For f(6):
(1/ ((6/4)+(36/4)-(216/16)-1)) /6 = -.041666666... or -1/24
For f(5):
(1/ ((5/4)+(25/4)-(125/16)-1)) / 5 = -0.152380952... or -16/105
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MAPLE
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f(n) := n -> (1/((n/4)+(n^2/4)-(n^3/16)-1))/n;
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CROSSREFS
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Cf. A052762 A072346.
Sequence in context: A132696 A056965 A062047 this_sequence A136679 A070929 A007394
Adjacent sequences: A117462 A117463 A117464 this_sequence A117466 A117467 A117468
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KEYWORD
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frac,nonn,uned
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AUTHOR
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steven j. forsberg (steven.forsberg(AT)ttu.edu), Apr 25 2006
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