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%I #13 Mar 09 2015 01:21:29
%S 1,0,1,0,21,266,2843,55932,884756,13816633,283194588,5375499165,
%T 125889124371,3202887665805,80542392920980,2270543992935431,
%U 64253268814048352,1892633465941308859,59116753827795287519,1886846993941912938452
%N Number of partitions of n^4 into n distinct nonzero squares.
%H Robert Gerbicz, May 09 2008, <a href="/A133105/b133105.txt">Table of n, a(n) for n = 1..20</a>
%e a(3)=1 because there is exactly one way to express 3^4 as the sum of 3 distinct nonzero squares: 81 = 1^2 + 4^2 + 8^2.
%o (PARI) a(i, n, k)=local(s, j); if(k==1, if(issquare(n) && n<i^2, return(1), return(0)), s=0; for(j=ceil(sqrt(n/k)), min(i-1, floor(sqrt(n-k+1))), s+=a(j, n-j^2, k-1)); return(s)) for(n=1,50, m=n^4; k=n; print1(a(m+1, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
%Y Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451.
%Y Cf. A133104 (number of ways to express n^4 as a sum of n nonzero squares), A133102 (number of ways to express n^3 as a sum of n distinct nonzero squares).
%K nonn
%O 1,5
%A _Hugo Pfoertner_, Sep 12 2007
%E a(10) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
%E a(11) onwards from _Robert Gerbicz_, May 09 2008
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