the new fibbonaci

Number Theory Level 3

assume a sequence "new fibbonaci" if it fullfills that the first and the second number is 1 , and the next number is the sum of the squares of the previous two number

example of the first few series are 1 , 1 , 2 , 5 , 29 , .....

find the remainder when the 10-th term is divided by 10.