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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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5
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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.
The g.f. -z**3*(1+2*z**2+2*z**3)/(-1+z-2*z**2+z**4+3*z**5+z**3) conjectured by Simon Plouffe in his 1992 dissertation is wrong since it produces negative terms. - N. J. A. Sloane, May 13 2008
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REFERENCES
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S. A. Burr, B. Gr\"{u}nbaum and N. J. A. Sloane, The Orchard Problem, Geometriae Dedicata, 2 (1974), 397-424.
M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, Chap. 22.
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).
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LINKS
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Table of n, a(n) for n=1..20.
P. Berloquin, a(12) >= 7 (from an article in Jeux & Strategies from 1983 - see Fig. 10)
S. A. Burr, B. Gr\"{u}nbaum and N. J. A. Sloane, The Orchard Problem, Geometriae Dedicata, 2 (1974), 397-424.
Du, Zhao Hui, Code to verify a(13) to a(16) for orchard planting problem
Xianzu Lin, Illustration showing that a(20) >= 23 [The points S and T are at infinity]
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Orchard-Planting Problem.
Link to one of the optimal results from 13~17 trees [From Du, Zhao Hui, Nov 11 2008]
Author?, A chinese webpage for the problem [From Du, Zhao Hui, Dec 17 2009]
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CROSSREFS
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Cf. A003035, A008997.
Sequence in context: A117752 A214045 A172992 * A218933 A096981 A035541
Adjacent sequences: A006062 A006063 A006064 * A006066 A006067 A006068
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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a(13) - a(15) from Du, Zhao Hui, Aug 24 2008
a(17) from Du, Zhao Hui, Nov 11 2008
a(18) from Du, Zhao Hui, Nov 25 2008
a(19) from Du, Zhao Hui, Dec 17 2009
a(20) from Du, Zhao Hui, Feb 01 2010
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STATUS
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approved
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