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%I #28 Feb 03 2021 15:39:27
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%T 0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,1,1,0,1,1,0,
%U 0,0,1,1,0,0,1,1,0,0,3,1,0,1,0,0,1,1,1,1,0,0,2,1,0,1,2,2,0,0,1,2,0,0,3,0,0,2,1,1
%N Number of partitions of n into 4 distinct nonzero squares.
%H Alois P. Heinz, <a href="/A025443/b025443.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) = [x^n y^4] 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`(t*i^2<n, 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), 4):
%p seq(a(n), n=0..150); # _Alois P. Heinz_, Feb 07 2013
%t b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[t*i^2<n, 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, 4]; Table[a[n], {n, 0, 150}] (* _Jean-François Alcover_, Feb 29 2016, after _Alois P. Heinz_*)
%Y Cf. A025428 (not necessarily distinct), A025376-A025394 (subsequences), A025417 (greedy inverse).
%Y Column k=4 of A341040.
%K nonn,look
%O 0,79
%A _David W. Wilson_
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