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

0,53

Comments

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

Links

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

Formula

a(n) <= A025428(n).

Example

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].

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);

Crossrefs

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

Sequence in context: A309887 A395033 A317595 * A263753 A303877 A112743

Adjacent sequences: A385857 A385858 A385859 * A385861 A385862 A385863

Keyword

nonn

Author

Felix Huber, Jul 22 2025

Status

approved