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Search: id:A133105
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| A133105 |
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Number of partitions of n^4 into n distinct nonzero squares. |
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+0
3
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| 1, 0, 1, 0, 21, 266, 2843, 55932, 884756, 13816633, 283194588, 5375499165, 125889124371, 3202887665805, 80542392920980, 2270543992935431, 64253268814048352, 1892633465941308859, 59116753827795287519, 1886846993941912938452
(list; graph; listen)
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OFFSET
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1,5
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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..20
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EXAMPLE
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a(3)=1 because there is exactly one way to express 3^4 by 3 distinct squares: 81=1^2+4^2+8^2.
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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^4; 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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Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451 Cf. A133104 [ways to express n^4 by n squares], A133102 [ways to express n^3 by n distinct squares].
Sequence in context: A133717 A056282 A000770 this_sequence A032535 A022745 A004324
Adjacent sequences: A133102 A133103 A133104 this_sequence A133106 A133107 A133108
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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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a(10) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
a(11) onwards from Robert Gerbicz (robert.gerbicz(AT)gmail.com), May 09 2008
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