# Are genotypes with the same two alleles equivalent even if the alleles come from different parents?

I am looking at the following question

If $m$ alleles may occur at a given locus, how many distinct diploid genotypes are possible at that locus?

The obvious answer is that there their is $m$ possible paternal alleles and $m$ possible maternal alleles so the solution is $m^2$. However this considers inheriting allele $a$ maternally and allele $A$ paternally as the same as inheriting $a$ paternally and $A$ maternally.

If they are considered distinct we have double counted all matchings apart from matchings where the same allele is inherited maternally and paternally so I think the answer to the question if $Aa$ is the same as $aA$ would be $\frac{m(m-1)}{2}+m$

My question is which if any of my interpretations is correct?

• Okay @GriffinEvo, so if we have 3 alleles then we have 9 genotypes, 6 of which are distinct? If we had two loci one with 2 alleles and another with 3 alleles would the number of distinct genotypes be $3 \times 6 = 18$ (just to check I understand) Apr 8 '15 at 13:14
If you have genomic imprinting then $k^n=m^2$ (with k=m and n=2 because of diploidy) is correct as inheriting a from the father and b from the mother (i.e. ab) is not equivalent to inheriting b from the father and a from the mother (i.e. ba). For 3 alleles (a,b,c) you have 9 possible genotypes (aa,ab,ac,ba,bb,bc,ca,cb,cc).
Under no genomic imprinting, ab and ba are equivalent. This is equivalent of calculating the number of elements of a triangular matrix which is $\frac{(m+1)*m}{2}$. So for m=3, you have 6 possible genotypes (aa,ab,ac,bb,bc,cc), for m=4 you have 10 possibilities (aa,ab,ac,ad,bb,bc,bd,cc,cd,dd) etc...