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

%I A347534 #19 Oct 25 2022 20:35:51
%S A347534 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 A347534 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 A347534 1,2,1,0,0,1,3,1,0,2,1,0,1,2,1,1,1,2,2
%N A347534 Number of partitions of n into at most 3 distinct squares.
%H A347534 Alois P. Heinz, <a href="/A347534/b347534.txt">Table of n, a(n) for n = 0..20000</a>
%H A347534 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A347534 a(n) = Sum_{k=0..3} A341040(n,k). - _Alois P. Heinz_, Sep 08 2021
%t A347534 a[n_] := IntegerPartitions[n, 3, Select[Range[n], IntegerQ@Sqrt[#]&]] // Select[#, Union[#] == Sort[#]&]& // Length;
%t A347534 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Sep 13 2021 *)
%Y A347534 Cf. A000290, A025435, A025442, A033461, A341040.
%K A347534 nonn
%O A347534 0,26
%A A347534 _Ilya Gutkovskiy_, Sep 08 2021