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A117655
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A simulation of a Fibonacci sequence as a von Bertalanff's curve population: f[t]=(A-B*Exp[t/3])^3.
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1
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0, 1, 0, 0, 0, 0, 1, 3, 12, 34, 54, 64, 69, 71, 71, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Often called the "fish weight" equation von Bertalanffy's curve is based on ideas of surface area to weight by volume in mass populations. It is another kind of sigmoid population saturation besides Pearl's Sigmoid.
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REFERENCES
| Ludwig von Bertalanffy, General Systems Theory, George Braziller publisher, New York, 1968, page 174-5
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FORMULA
| f[n]=(A+B/(f[n-1]+f[n-1))^(1/3))^3 a(n) =Flood[f[n]]
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MATHEMATICA
| Clear[f] f[0] = 0; f[1] = 1; f[n_] := f[n] = N[(5 - 4.37/(f[n - 1] + f[n - 2])^(1/3))^3] a = Table[Abs[Floor[f[n]]], {n, 0, 25}] ListPlot[a, PlotJoined -> True, PlotRange -> All]
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CROSSREFS
| Cf. A000045.
Sequence in context: A054610 A183468 A196234 * A081423 A184705 A060298
Adjacent sequences: A117652 A117653 A117654 * A117656 A117657 A117658
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 11 2006
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