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A133105
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Number of partitions of n^4 into n distinct nonzero squares.
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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
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OFFSET
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1,5
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LINKS
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EXAMPLE
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a(3)=1 because there is exactly one way to express 3^4 as the sum of 3 distinct nonzero squares: 81 = 1^2 + 4^2 + 8^2.
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PROG
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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. A133104 (number of ways to express n^4 as a sum of n nonzero squares), A133102 (number of ways to express n^3 as a sum of n distinct nonzero squares).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(10) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007
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STATUS
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approved
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