A347534 Number of partitions of n into at most 3 distinct squares.

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

Offset: 0

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A025435, A025442, A033461, A341040.

Programs

Mathematica

a[n_] := IntegerPartitions[n, 3, Select[Range[n], IntegerQ@Sqrt[#]&]] // Select[#, Union[#] == Sort[#]&]& // Length;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 13 2021 *)

Formula

a(n) = Sum_{k=0..3} A341040(n,k). - Alois P. Heinz, Sep 08 2021