Let me introduce you to the unicellular organism code-named as:\(Riru\). A cell of \(Riru\), at the end of each day, fragments into \(r\) daughter cells, where \(1\le r\le 4\). The probability of \(r\) taking a certain numerical value, is directly proportional to that value itself. Al the beginning of day \(1\), one cell of \(Riru\) was present in an isolated habitat, with plenty of resources. Find the average \(Riru\) population at the beginning of day \(21\).
###### This is part of my set Powers of the ordinary.

###### Image Credit: Wikimedia Volvocales

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