This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133102 #16 May 31 2025 15:06:42 %S A133102 1,0,0,0,0,3,5,20,56,112,268,618,1922,8531,29021,100407,321531,899618, %T A133102 2937312,9295401,31615059,117365818,403433963,1417579281,4848439367, %U A133102 15960316056,55180971700,190251417034,670818005444,2429973932322 %N A133102 Number of partitions of n^3 into n distinct nonzero squares. %H A133102 Robert Gerbicz, May 09 2008, <a href="/A133102/b133102.txt">Table of n, a(n) for n = 1..40</a> %e A133102 a(6) = 3 because there are 3 ways to express 6^3 = 216 as a sum of 6 distinct nonzero squares: 216 = 1^2 + 2^2 + 4^2 + 5^2 + 7^2 + 11^2 = 1^2 + 3^2 + 5^2 + 6^2 + 8^2 + 9^2 = 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 9^2. %o A133102 (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)) %o A133102 for(n=1,50, m=n^3; k=n; print1(a(m+1, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007 %Y A133102 Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451. %Y A133102 Cf. A133103 (number of ways to express n^3 as a sum of n nonzero squares), A133105 (number of ways to express n^4 as a sum of n distinct nonzero squares). %K A133102 nonn %O A133102 1,6 %A A133102 _Hugo Pfoertner_, Sep 12 2007 %E A133102 2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007 %E A133102 More terms from _Robert Gerbicz_, May 09 2008