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%I #13 Mar 09 2015 02:09:17
%S 1,1,2,1,10,34,156,734,3599,18956,99893,548373,3078558,17510598,
%T 101960454,599522778,3565904170,21438347021,129905092421,794292345434,
%U 4890875249113,30326545789640,189195772457341,1187032920371427
%N Number of partitions of n^3 into n nonzero squares.
%H Robert Gerbicz, May 09 2008, <a href="/A133103/b133103.txt">Table of n, a(n) for n = 1..40</a>
%e a(2)=1 because the only way to express 2^3 = 8 as a sum of two squares is 8 = 2^2 + 2^2.
%e a(3)=2 because 3^3 = 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2.
%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^3; 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. A133102 (number of ways to express n^3 as a sum of n distinct nonzero squares), A133104 (number of ways to express n^4 as a sum of n nonzero squares).
%K nonn
%O 1,3
%A _Hugo Pfoertner_, Sep 11 2007
%E 2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
%E More terms from _Robert Gerbicz_, May 09 2008
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