Brain-Teaser 459

From The Sunday Times, 8th March 1970 [link]

Grandpa was as pleased as Punch when he heard that his large flock of grandchildren would be there at his birthday party, but he couldn’t remember how many there were. So he wrote to his youngest daughter, who knew he liked problems, and got back the answer:

“There are just enough children to arrange them in pairs in such a way that the square of the age of the first of a pair added to thrice the square of the age of the second give the same total for every pair. The eldest is still a teenager. You remember that I have twins one year old.”

How many grandchildren are there?