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%I #10 Jul 15 2015 15:13:57
%S 1,0,3,1,49,732,9659,190169,3225654,61896383,1360483727,30969769918,
%T 778612992660,20749789703573,579672756740101,17115189938667708,
%U 525530773660159970,16825686497823918869,561044904645283065043,19368002907483932784642
%N Number of partitions of n^4 into n nonzero squares.
%e a(3)=3 because there are 3 ways to express 3^4 = 81 as a sum of 3 nonzero squares: 81 = 1^2 + 4^2 + 8^2 = 3^2 + 6^2 + 6^2 = 4^2 + 4^2 + 7^2.
%e a(4)=1 because the only way to express 4^4 = 256 as a sum of 4 nonzero squares is 256 = 8^2 + 8^2 + 8^2 + 8^2.
%o (PARI) a(i, n, k)=local(s, j); if(k==1, if(issquare(n), return(1), return(0)), s=0; for(j=ceil(sqrt(n/k)), min(i, 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, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
%Y Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451.
%Y Cf. A133105 (number of ways to express n^4 as a sum of n distinct nonzero squares), A133103 (number of ways to express n^3 as a sum of n nonzero squares).
%K nonn
%O 1,3
%A _Hugo Pfoertner_, Sep 11 2007
%E a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
%E a(10) onwards from _Robert Gerbicz_, May 09 2008
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