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Search: id:A119395
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| A119395 |
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Number of nonnegative integer solutions to the equation x^2+3y^2=n. |
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+0
2
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| 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 3, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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The number of integer solutions is given by A033716.
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FORMULA
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For n>0, a(n)=(A033716(n)+2)/4 if n is a square or a triple of a square; otherwise a(n)=A033716(n)/4. Alternatively, a(n)=ceil(A033716(n)/4).
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PROGRAM
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(PARI) { A033716(n) = local(f, B); f=factorint(n); B=1; for(i=1, matsize(f)[1], if(f[i, 1]%3==1, B*=f[i, 2]+1); if(f[i, 1]%3==2, if(f[i, 2]%2, return(0)))); if(n%4, 2*B, 6*B) } { a(n) = ceil(A033716(n)/4) }
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CROSSREFS
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Cf. A033716, A096936.
Sequence in context: A102082 A030199 A005089 this_sequence A087476 A035162 A121454
Adjacent sequences: A119392 A119393 A119394 this_sequence A119396 A119397 A119398
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), May 16 2006
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