A385860 a(n) is the number of distinct multisets of sides of quadrilaterals with perimeter n, where all four sides are squares.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 3, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 0, 2, 1, 1, 1

Offset: 0

Author

Felix Huber, Jul 22 2025

Keywords

• nonn

Comments

a(n) is the number of partitions of n into 4 nonzero squares < n/2.

Examples

			The a(51) = 1 multiset is [1, 9, 16, 25].
The a(52) = 3 multisets are [1, 1, 25, 25], [4, 16, 16, 16] and [9, 9, 9, 25].
		

Links

• Felix Huber, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A000414, A000534, A025428, A062890, A385736.

Programs

Maple

# After Alois P. Heinz (A025428)
b:=proc(n,i,t)
    option remember;
    `if`(n=0,`if`(t=0,1,0),`if`(i<1 or t<1, 0, b(n,i-1,t)+`if`(i^2>n,0,b(n-i^2,i,t-1))))
    end:
A385860:=n->b(n,floor(sqrt((n-1)/2)),4):
seq(A385860(n),n=0..87);

Formula

a(n) <= A025428(n).