%I
%S 0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,
%T 1,0,0,1,0,0,1,1,0,0,0,1,0,0,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0,2,0,0,
%U 1,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,2,0,0,0,1,1,0,0,0,0,0,0,1,0,0,1,1,0,0,1,0,1,0
%N Number of partitions of n into 2 distinct nonzero squares.
%H T. D. Noe, <a href="/A025441/b025441.txt">Table of n, a(n) for n = 0..10000</a>
%H Michael Gilleland, <a href="/selfsimilar.html">Some SelfSimilar Integer Sequences</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(A025302(n)) = 1.  _Reinhard Zumkeller_, Dec 20 2013
%F a(n) = Sum_{ m: m^2n } A157228(n/m^2).  _Andrey Zabolotskiy_, May 07 2018
%F a(n) = [x^n y^2] Product_{k>=1} (1 + y*x^(k^2)).  _Ilya Gutkovskiy_, Apr 22 2019
%p P:=proc(n) local a,x; a:=1; x:=0; while a^2<trunc(n/2)
%p do if frac(sqrt(na^2))=0 then x:=x+1; fi; a:=a+1; od; x; end:
%p seq(P(i),i=1..100); # _Paolo P. Lava_, Mar 12 2018
%t Table[Count[PowersRepresentations[n, 2, 2], pr_ /; Unequal @@ pr && FreeQ[pr, 0]], {n, 0, 107}] (* _JeanFrançois Alcover_, Mar 01 2019 *)
%o (Haskell)
%o a025441 n = sum $ map (a010052 . (n )) $
%o takeWhile (< n `div` 2) $ tail a000290_list
%o  _Reinhard Zumkeller_, Dec 20 2013
%o (PARI) a(n)=if(n>4,sum(k=1,sqrtint((n1)\2),issquare(nk^2)),0) \\ _Charles R Greathouse IV_, Jun 10 2016
%o (PARI) a(n)=if(n<5,return(0)); my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f[, 1], if(f[i, 1]%4==1, t*=f[i, 2]+1, if(f[i, 2]%2, return(0)))); if(t%2, t(1)^v, t)/2issquare(n/2) \\ _Charles R Greathouse IV_, Jun 10 2016
%Y Cf. A060306 gives records; A052199 gives where records occur.
%Y Cf. A000161, A000290, A010052, A025435, A157228, A053866, A145393.
%K nonn
%O 0,66
%A _David W. Wilson_
