A347534 - OEIS

%I #19 Oct 25 2022 20:35:51

%S 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,

%T 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,

%U 1,2,1,0,0,1,3,1,0,2,1,0,1,2,1,1,1,2,2

%N Number of partitions of n into at most 3 distinct squares.

%H Alois P. Heinz, <a href="/A347534/b347534.txt">Table of n, a(n) for n = 0..20000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F a(n) = Sum_{k=0..3} A341040(n,k). - _Alois P. Heinz_, Sep 08 2021

%t a[n_] := IntegerPartitions[n, 3, Select[Range[n], IntegerQ@Sqrt[#]&]] // Select[#, Union[#] == Sort[#]&]& // Length;

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Sep 13 2021 *)

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

%K nonn

%O 0,26

%A _Ilya Gutkovskiy_, Sep 08 2021