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Search: id:A133104
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| A133104 |
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Number of partitions of n^4 into n nonzero squares. |
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+0
3
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| 1, 0, 3, 1, 49, 732, 9659, 190169, 3225654, 61896383, 1360483727, 30969769918, 778612992660, 20749789703573, 579672756740101, 17115189938667708, 525530773660159970, 16825686497823918869, 561044904645283065043, 19368002907483932784642
(list; graph; listen)
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OFFSET
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1,3
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EXAMPLE
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a(3)=3 because there are 3 ways to express 3^3=81 by a sum of 3 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 by 4 squares is 256=8^2+8^2+8^2+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), 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
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CROSSREFS
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Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451. Cf. A133105 [ways to express n^4 by n distinct squares], A133103 [ways to express n^3 by n squares].
Sequence in context: A104097 A098341 A010292 this_sequence A095988 A082525 A016482
Adjacent sequences: A133101 A133102 A133103 this_sequence A133105 A133106 A133107
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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 11 2007
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EXTENSIONS
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a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
a(10) onwards from Robert Gerbicz (robert.gerbicz(AT)gmail.com), May 09 2008
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