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 A133104 Number of partitions of n^4 into n nonzero squares. 2
 1, 0, 3, 1, 49, 732, 9659, 190169, 3225654, 61896383, 1360483727, 30969769918, 778612992660, 20749789703573, 579672756740101, 17115189938667708, 525530773660159970, 16825686497823918869, 561044904645283065043, 19368002907483932784642 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE 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. 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. PROG (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 CROSSREFS Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451. 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). Sequence in context: A098341 A223173 A010292 * A322730 A292425 A095988 Adjacent sequences:  A133101 A133102 A133103 * A133105 A133106 A133107 KEYWORD nonn AUTHOR Hugo Pfoertner, Sep 11 2007 EXTENSIONS a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007 a(10) onwards from Robert Gerbicz, May 09 2008 STATUS approved

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)