Father's age from nine evenly spaced children

A father has nine children whose ages are distinct whole numbers forming an arithmetic progression (equal gaps between successive births). The squares of the children's ages add up to the square of the father's age, and the father is no older than $60$. How old is he?

48. With middle age $m$ and gap $s$, the sum of squares is $9m^2+60s^2=d^2$. Divisibility by $3$ and the size bound $d\ge14s$ force $s=3$, leaving $(d/3)^2-m^2=60$; the only fit with positive ages is $m=14$, $d=48$ (ages $2,5,\dots,26$).