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, 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.

Links

Table of n, a(n) for n=0..25.

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

Adjacent sequences: A117646 A117647 A117648 * A117650 A117651 A117652

Keyword

nonn,uned

Author

Roger L. Bagula, Apr 10 2006

Status

approved