We use some recent results concerning universal mixed sums of squares and triangular numbers in order to prove that all positive integers n of the form    can be written as a sum of three squares of numbers of a given shape. We also use some -partitions in order to obtain formulas for the number of some restricted compositions of a positive integer n in which any partial sum of the parts is a given mixed sum of squares and triangular numbers.

composition, Diophantine equation, partition,

-partition, quadratic form, representation, square number, triangular number.