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A069981
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Hermite's problem: number of positive integral solutions to x + y + z = n subject to x <= y + z, y <= z + x and z <= x + y.
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3
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0, 0, 0, 1, 3, 3, 7, 6, 12, 10, 18, 15, 25, 21, 33, 28, 42, 36, 52, 45, 63, 55, 75, 66, 88, 78, 102, 91, 117, 105, 133, 120, 150, 136, 168, 153, 187, 171, 207, 190, 228, 210, 250, 231, 273, 253, 297, 276, 322, 300, 348, 325, 375, 351, 403, 378, 432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, Europ. J. Combin., 22 (2001), 887-904.
G. Polya and G. Szego, Problems and Theorems in Analysis I, Springer-Verlag, Part I, Chap. 1, Problem 31.
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LINKS
| William A. Tedeschi, Table of n, a(n) for n=0..10000
G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 16.
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FORMULA
| G.f.: q^3*(1+2*q-2*q^2)/(1-q)/(1-q^2)^2. a(n) = (n+8)(n-2)/8 for n even, (n^2-1)/8 for n odd.
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MATHEMATICA
| f[n_]:=If[EvenQ[n], ((n+8)(n-2))/8, (n^2-1)/8]; Join[{0}, Array[f, 60]] (* From Harvey P. Dale, Jul 26 2011 *)
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CROSSREFS
| Cf. A005044.
Sequence in context: A146970 A078708 A096273 * A000199 A201932 A161771
Adjacent sequences: A069978 A069979 A069980 * A069982 A069983 A069984
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 06 2002
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