I'm working in bioinformatics, but my computational skills far outstrip my knowledge of biology or genomics. So forgive the dumb question.

According to the VCF specification, the INFO column for each coordinate [CHROM, POS] can contain values for

AC : allele count in genotypes, for each ALT allele, in the same order as listed
AF : allele frequency for each ALT allele in the same order as listed: use this when estimated from primary data, not called genotypes
AN : total number of alleles in called genotypes

For example, I'm working with the the VCF file you can download from Kaviar.

I think I understand how to calculate those numbers from raw sequences from a pileup. If for a given coordinate [CHROM, POS], $N_0$ is the number of hits for the reference allele, and $N_i$ is the number of hits for the $ith$ variant (maybe only one), then the allele frequency for the $ith$ variant is

$$AF_i = \frac{N_i}{\sum_0^n N_i}$$

Or, since biostars thinks that math only for people who don't do biology,

AF_i = N_i/sum(all N_i, i = 0...n)

I'm assuming that AC is the same as N_i (listed in the row for that variant) and that AN is the sum of N_i, i=0...n. So the phrase "total number of alleles in the dataset" would mean "total number of hits to coordinate [CHROM, POS] for any allele. And by "hit" I mean an aligned sequence fragment that includes that coordinate.

But I may not be taking into account the caveat for AF: "use this when estimated from primary data, not called genotypes."

Am I correctly understanding AF, AC, and AN in Kaviar?