Are codons in RNA layered? Are we misinterpreting RNA codons? I am analyzing nucleotide base-pair patterns in RNA and DNA, and had a thought about RNA and DNA (Let me first state though, I am not a biologist; I am an algorithmatician, employing a sort of recursive sequential neural network).
In any event, I was wondering if we are misinterpreting the way that we look at codons in RNA.  Are we?  Are we missing something when we interpret them the way that we do?  A picture is worth a thousand words, so I made a powerpoint slide of my question and screen captured it.  It highlights the specific question I am asking, which is: are codons layered?
Why is this important to me?  When I look at patterns, I know for a fact that unless it is the end of the sequence (a stop codon) that if I have a U-nucleotide, then the next two nucleotides cannot be AA, AG, nor GA.  Additionally, I know that unless there is a U-nucleotide, the sequence will definitely not end in two or less nucleotides.  This is what got me to wondering if there indeed is layered information in the combination of nucleotides.  Please see the picture.
So if we have (as in the picture) an RNA sequence:
AUGGUCAGUCCAUAA
We might interpret that as 5 codons {Methionine, Valine, Serine, Proline, STOP}
But what if there are actually 13 codons: {Methionine, Tryptophan, Glycine, Valine, Serine, Glutamine, Serine, Valine, Serine, Proline, Histidine, Isoleucine, STOP}
This relates to the concept of the reading frame, which is the point at which you start dividing 3-letter sequences into codons. As you point out, there are multiple ways to divide a string of amino acids into triplets - in fact, there are six unique ways, found by shifting the start letter by one three times, and doing the same but reading in reverse.
Typically, there is one commonly used frame which can be transcribed and turned into protein, called the open reading frame. But it is not unheard of for a single piece of DNA to encode multiple, overlapping genes, depending on where you start reading it. So, the sequence you show cannot encode 13 amino acids in a single string, but it can encode three different strings, one of which has 5 amino acids and the other two which have 4 amino acids each.
See Multiple Reading Frames at Wikipedia, which shows the following example of a single piece of human DNA which encodes two different genes, MT-ATP6 and MT-ATP8.