Unfortunately, with each parent being from a different reg. the resulting foal can not be reg. in either. The parents must be from the same reg to register the foal in that registry (both must be A&R to reg. A&R and under 34", Or both must be A and 34" or under to be A , or both must be 38" or under and R reg. to have an R Reg. foal). The stallion can be R hardshipped, or the mare, as long as she is 34" or under can be A hardshipped ,all this must be done before the foal is born or there will be other fees too, then the foal can be reg., but this can get pricey.
As things stand the way it is, the foal is unregisterable.