How is patau syndrome inherited? From mom or dad or both?

It's not. This and the other forms of trisomy happen by chance (new event) they are not inherited. The egg & sperm are both supposed to bring one each of the parents 23 chromosomes so the new baby has 46 (23 pairs). With trisomies, either the egg or sperm brings an extra so you have 23 pairs plus one.The extra chromosome ends up in every cell of the body and confuses the cells metabolism, causing defects.
Non-disjunction. The majority of cases of the lethal patau or trisomy 13 syndrome are caused by nondisjunction (47, +13) related to advanced maternal age. Robertsonian translocations of either parent can increase the risk for that couple, although most affected embryos die in utero.