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Search: id:A133102
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| A133102 |
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Number of partitions of n^3 into n distinct nonzero squares. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,6
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LINKS
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Robert Gerbicz (robert.gerbicz(AT)gmail.com), May 09 2008, Table of n, a(n) for n = 1..40
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EXAMPLE
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a(6)=3 because there are 3 ways to express 6^3=216 as a sum of 6 distinct 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.
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PROGRAM
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(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
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CROSSREFS
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A133103 Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451 Cf. A133103 [ways to express n^3 by n squares], A133105 [ways to express n^4 by n distinct squares].
Adjacent sequences: A133099 A133100 A133101 this_sequence A133103 A133104 A133105
Sequence in context: A077458 A062577 A076149 this_sequence A066902 A007363 A103991
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 12 2007
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EXTENSIONS
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2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
More terms from Robert Gerbicz (robert.gerbicz(AT)gmail.com), May 09 2008
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