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A133102
Number of partitions of n^3 into n distinct nonzero squares.
3
1, 0, 0, 0, 0, 3, 5, 20, 56, 112, 268, 618, 1922, 8531, 29021, 100407, 321531, 899618, 2937312, 9295401, 31615059, 117365818, 403433963, 1417579281, 4848439367, 15960316056, 55180971700, 190251417034, 670818005444, 2429973932322
OFFSET
1,6
LINKS
Robert Gerbicz, May 09 2008, Table of n, a(n) for n = 1..40
EXAMPLE
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.
PROG
(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^3; k=n; print1(a(m+1, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
CROSSREFS
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).
Sequence in context: A295361 A295357 A076149 * A197156 A171864 A256093
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 12 2007
EXTENSIONS
2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
More terms from Robert Gerbicz, May 09 2008
STATUS
approved