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Search: id:A067754
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| A067754 |
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Number of unordered primitive solutions to xy+xz+yz=n. |
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+0
4
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| 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 4, 2, 3, 2, 3, 3, 4, 2, 4, 4, 2, 4, 3, 2, 4, 4, 4, 3, 4, 3, 6, 3, 2, 4, 6, 4, 5, 4, 3, 4, 4, 3, 6, 4, 3, 4, 6, 3, 4, 4, 6, 6, 4, 2, 7, 4, 4, 5, 6, 3, 6, 6, 3, 5, 6, 4, 8, 4, 3, 6, 6, 4, 6, 4, 6, 6, 4, 3, 7, 6, 4, 6, 8, 4, 7, 6, 6, 4, 4, 5, 10, 6, 3, 5, 6, 3
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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For n = m^2 this is the number of root Descartes quadruples (-m,b,c,d).
An upper bound on the number of solutions appears to be 1.5*sqrt(n). - T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
R. L. Graham, J. C. Lagarias, C. L. Mallows, A. R. Wilks and C. Yan, Apollonian circle packings: Number theory
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FORMULA
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a(n)=A066360(n)+A007875(n) - T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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EXAMPLE
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a(9)=2 because of (0,1,9) and (1,1,4) (but not (0,3,3)).
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MATHEMATICA
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Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z] && GCD[x, y, z]==1, cnt++ ], {x, 0, Sqrt[n/3]}, {y, Max[1, x], Sqrt[x^2+n]-x}]; cnt, {n, 100}] - T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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CROSSREFS
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Cf. A067751, A067752, A067753.
Sequence in context: A156642 A155124 A138033 this_sequence A025851 A125688 A060508
Adjacent sequences: A067751 A067752 A067753 this_sequence A067755 A067756 A067757
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KEYWORD
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easy,nonn
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AUTHOR
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Colin L. Mallows (colinm(AT)avaya.com), Jan 31 2002
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Jun 14 2006
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