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A117649
A Verhulst/ Pearl's equation type simulation of a sigmoid population sequence using a base A000045 model ( the populations are not smooth curves but integers).
0
0, 1, 1, 1, 2, 4, 7, 11, 17, 25, 35, 47, 58, 69, 78, 85, 90, 93, 96, 97, 98, 99, 99, 100, 100, 100
OFFSET
0,5
COMMENTS
Constants L=200 and A=199 adjust how fast and high the plateau is reached. This type of model is more realistic than the Fibonacci rabbits, but basically starts out with the same kind of variance.
FORMULA
f[n]=L/(1+A/(f[n-1]+f[n-2))) a(n) = Floor[f(n))
MATHEMATICA
lear[f, M, v] f[0] = 0; f[1] = 1; f[n_] := f[n] = N[200/(1 + 199/(f[n - 1] + f[n - 2]))] Table[Abs[Floor[f[n]]], {n, 0, 25}] ListPlot[%, PlotJoined -> True, PlotRange -> All]
CROSSREFS
Cf. A000045.
Sequence in context: A073471 A308825 A266901 * A028291 A067997 A175491
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Apr 10 2006
STATUS
approved