# How to resolve this equation for $f(n)$ without using $f(n-1)$

I have an equation related to some work I'm doing on Poisson distribution where I'm calculating a sequence of 100 values between a minimum and maximum value which is set by another formula. Unfortunately I don't really understand this area of maths, but I'm trying to resolve this equation to use in a computer calculation.

Let $m$ be the minimum value and $M$ be the maximum value (which are given).

$n$, $m$ and $M$ are all integers. f(n) is also rounded to an integer value.

For $n=1$, $$f(n) = \min(m,1)$$

For values of $1<n\leq100$ this is the formulae $$\large{ f(n) = \min\Biggl\lgroup\biggl\lgroup\frac{M}{f(n-1)}\biggr\rgroup^{\frac{1}{101-n}} \cdot (n-1) , n\Biggr\rgroup }$$

My question is - is there a way to implement this function/equation that doesn't rely on knowing the value of $f(n-1)$ - knowing $n$, $M$, and $m$.

An example sequence for $m=1$, $M=847$ is at http://pastebin.com/PvQgNg7i

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Apologies if my terminology and markup is bad - I've not done proper maths in over 10 years! It's my first question on here, so be gentle :) – x3ja Feb 14 '13 at 0:11
Hey, not bad for someone so rusty! Anyway, one thing I could suggest is to try a few numerical values out and see how things behave. This is a tough-looking definition, but maybe there's an underlying pattern. – Ron Gordon Feb 14 '13 at 0:37
What is the nature of the max and min values? Are they integers, positive integers, or just any old real number? – apnorton Feb 14 '13 at 1:07
@rlgordonma - I can calculate the series in Excel. For $m=1$ & $M=847$, the values are as at pastebin.com/PvQgNg7i – x3ja Feb 14 '13 at 8:01
@anorton Good question - $n$, $m$, $M$ and $f(n)$ are all integers. There is some rounding that I've omitted - not sure how to show that. Essentially the first expression in the minimum (everything except the $, n$) is rounded to the nearest integer. Will add that to the question. – x3ja Feb 14 '13 at 8:03