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%I #22 Feb 03 2021 15:39:05
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,0,0,
%T 0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,2,0,0,1,1,0,
%U 0,2,1,0,0,0,2,1,0,2,1,0,0,1,0,1,1,0,2,0,0,2,2,1,0,1,2,0,0,0,2,0,0,3,0,0,1,2,1,1
%N Number of partitions of n into 3 distinct nonzero squares.
%H Alois P. Heinz, <a href="/A025442/b025442.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n)>0 <=> n is in A004432. - _M. F. Hasler_, Feb 03 2013
%F a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^(k^2)). - _Ilya Gutkovskiy_, Apr 22 2019
%p b:= proc(n,i,t) option remember; `if`(n=0, `if`(t=0,1,0),
%p `if`(i<1 or t<1, 0, `if`(i=1, 0, b(n,i-1,t))+
%p `if`(i^2>n, 0, b(n-i^2,i-1,t-1))))
%p end:
%p a:= n-> b(n, isqrt(n), 3):
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Feb 07 2013
%t b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1 || t<1, 0, If[i==1, 0, b[n, i-1, t]] + If[i^2 > n, 0, b[n-i^2, i-1, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 3]; Table[a[n], {n, 0, 120}] (* _Jean-François Alcover_, Oct 10 2015, after _Alois P. Heinz_ *)
%o (PARI) A025442(n)={sum(x=1,sqrtint(n\3),sum(y=x+1,sqrtint((n-1-x^2)\2),issquare(n-x^2-y^2)))} \\ - _M. F. Hasler_, Feb 03 2013
%Y Cf. A024803, A025339, A001974, A004432.
%Y Column k=3 of A341040.
%K nonn
%O 0,63
%A _David W. Wilson_
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