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A093115
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Number of partitions of n^2 into squares not greater than n.
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4
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1, 1, 1, 1, 5, 7, 10, 13, 17, 108, 159, 228, 317, 430, 572, 748, 5753, 8125, 11266, 15376, 20672, 27430, 35942, 46575, 59717, 523905, 708028, 946875, 1253880, 1645224, 2140099, 2761318, 3535658, 4494602, 5674753, 7118724, 69766770, 90940578, 117756370
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OFFSET
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0,5
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..500
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FORMULA
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Coefficient of x^(n^2) in the series expansion of Product_{k=1..floor(sqrt(n))} 1/(1 - x^(k^2)). - Vladeta Jovovic, Mar 24 2004
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EXAMPLE
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n=6: 6^2 = 9*2^2 = 8*2^2+4*1^2 = 7*2^2+8*1^2 = 6*2^2+12*1^2 = 5*2^2+16*1^2 = 4*2^2+20*1^2 = 3*2^2+24*1^2 = 2*2^2+28*1^2 = 1*2^2+32*1^2 = 36*1^2, therefore a(6)=10.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))
end:
a:= proc(n) local r; r:= isqrt(n);
b(n^2, r-`if`(r^2>n, 1, 0))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Apr 15 2013
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CROSSREFS
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Cf. A093116, A092362, A001156, A037444, A078134.
Cf. A072925.
Cf. A072213, A161407. [Reinhard Zumkeller, Jun 10 2009]
Sequence in context: A196175 A112251 A089061 * A020936 A025074 A065503
Adjacent sequences: A093112 A093113 A093114 * A093116 A093117 A093118
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KEYWORD
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nonn,changed
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AUTHOR
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Reinhard Zumkeller, Mar 21 2004
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EXTENSIONS
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More terms from Vladeta Jovovic, Mar 24 2004
Corrected a(0) by Alois P. Heinz, Apr 15 2013
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STATUS
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approved
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