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A006065
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Maximal number of 4-tree rows in n-tree orchard problem.
(Formerly M0290)
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7
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0, 0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 7, 9, 10, 12, 15, 16, 18, 20, 23
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,7
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COMMENTS
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Maximum number of rows with exactly 4 trees in each row if there are n trees in the orchard.
For further references and links see A003035.
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, Chap. 22.
F. Levi, Geometrische Konfigurationen, Hirzel, Leipzig, 1929.
Xianzu Lin, A new result about orchard-planting problem, Preprint, 2005. [Shows a(20) >= 23.]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
For further references and links see A003035.
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LINKS
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P. Berloquin, a(12) >= 7 (from an article in Jeux & Strategies from 1983 - see Fig. 10).
S. A. Burr, B. Grünbaum and N. J. A. Sloane, The Orchard Problem, Geometriae Dedicata, 2 (1974), 397-424.
S. A. Burr, B. Grünbaum and N. J. A. Sloane, The Orchard Problem, Geometriae Dedicata, 2 (1974), 397-424.
Branko Grünbaum and J. F. Rigby, The real configuration (21_4), Journal of the London Mathematical Society 2.2 (1990): 336-346. [Shows a(21) >= 21.]
Ed Pegg, Jr., Mathpuzzxle Blog, Updated Feb 27 2020. [Gives new construction for n = 22]
Ed Pegg, Jr., Mathpuzzxle Blog, Updated Feb 27 2020. [Gives new construction for n = 22] (extract, local copy)
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FORMULA
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CROSSREFS
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Cf. A172992 (the same problem, but with integer-valued tree coordinates).
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KEYWORD
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nonn,hard,nice,more,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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