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A002848
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Maximal number of disjoint subsets {X,Y,Z} of {1, 2, ..., n} with X+Y=Z (as in A002849), with the property that n is in one of the subsets.
(Formerly M0295 N0106)
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5
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0, 0, 0, 1, 1, 2, 2, 3, 7, 15, 12, 30, 8, 32, 164, 21, 114, 867, 3226, 720, 4414, 24412, 4079, 31454, 3040, 25737, 252727, 20505, 191778, 2140186, 14554796, 1669221, 17754992, 148553131, 14708525, 177117401, 10567748, 138584026, 1953134982, 103372655
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OFFSET
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0,6
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REFERENCES
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R. K. Guy, ``Sedlacek's Conjecture on Disjoint Solutions of x+y= z,'' Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
R. K. Guy, ``Sedlacek's Conjecture on Disjoint Solutions of x+y= z,'' in Proc. Conf. Number Theory. Pullman, WA, 1971, pp. 221-223.
R. K. Guy, ``Packing [ 1,n ] with solutions of ax + by = cz; the unity of combinatorics,'' in Colloq. Internaz. Teorie Combinatorie. Rome, 1973, Atti Conv. Lincei. Vol. 17, Part II, pp. 173-179, 1976.
Richard K. Guy, The unity of combinatorics, in Proc. 25th Iran. Math. Conf., Tehran, (1994), Math. Appl. 329 (1994) 129-159, Kluwer Acad. Publ., Dordrecht, 1995.
Nigel Martin, Solving a conjecture of Sedlacek: maximal edge sets in the 3-uniform sumset hypergraphs, Discrete Mathematics, Volume 125, 1994, pp. 273-277.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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a(n) = A002849(n) for n == 0,3,7,10 (mod 12), 0 for n=1, and A002849(n)-A002849(n-1) otherwise. - Franklin T. Adams-Watters.
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EXAMPLE
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Examples from Alois P. Heinz, Feb 12 2010:
A002848(7) = 3:
[1, 3, 4], [2, 5, 7]
[1, 5, 6], [3, 4, 7]
[2, 3, 5], [1, 6, 7]
A002848(8) = 7:
[1, 3, 4], [2, 6, 8]
[1, 4, 5], [2, 6, 8]
[1, 6, 7], [3, 5, 8]
[2, 3, 5], [1, 7, 8]
[2, 4, 6], [1, 7, 8]
[2, 4, 6], [3, 5, 8]
[3, 4, 7], [2, 6, 8]
A002848(10) = 12:
[1, 4, 5], [2, 6, 8], [3, 7, 10]
[1, 4, 5], [3, 6, 9], [2, 8, 10]
[1, 5, 6], [3, 4, 7], [2, 8, 10]
[1, 6, 7], [4, 5, 9], [2, 8, 10]
[1, 7, 8], [2, 3, 5], [4, 6, 10]
[1, 8, 9], [2, 3, 5], [4, 6, 10]
[1, 8, 9], [2, 4, 6], [3, 7, 10]
[1, 8, 9], [2, 5, 7], [4, 6, 10]
[2, 4, 6], [3, 5, 8], [1, 9, 10]
[2, 6, 8], [3, 4, 7], [1, 9, 10]
[2, 6, 8], [4, 5, 9], [3, 7, 10]
[2, 7, 9], [3, 5, 8], [4, 6, 10]
See A002849 for further examples.
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CROSSREFS
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Cf. A002849, A108235, A161826.
Sequence in context: A060357 A064714 A152255 * A032257 A038075 A032236
Adjacent sequences: A002845 A002846 A002847 * A002849 A002850 A002851
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Edited by N. J. A. Sloane, Feb 10 2010, based on posting to the Sequence Fans Mailing List by Franklin T. Adams-Watters, Richard K. Guy, R. H. Hardin, Alois P. Heinz, Andrew Weimholt, Max Alekseyev and others.
a(32)-a(39) from Max Alekseyev, Feb 23 2012
Definition corrected by Max Alekseyev, Nov 16 2012
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STATUS
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approved
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