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A002848
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Number of maximal collections of pairwise 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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10
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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, 1431596750, 22374792451, 218018425976, 16852166906, 254094892254
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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," 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.
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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R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission]
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FORMULA
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EXAMPLE
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[1, 3, 4], [2, 5, 7]
[1, 5, 6], [3, 4, 7]
[2, 3, 5], [1, 6, 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]
[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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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