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Search: id:A006065
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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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+0
3
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| 0, 0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 7
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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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 S. Plouffe in his 1992 dissertation is wrong since it produces negative terms. - njas, 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.]
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LINKS
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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.
Xianzu Lin, Illustration showing that a(20) >= 23 [The points S and T are at infinity]
S. 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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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CROSSREFS
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Cf. A003035, A008997.
Sequence in context: A098382 A098180 A117752 this_sequence A096981 A035541 A060966
Adjacent sequences: A006062 A006063 A006064 this_sequence A006066 A006067 A006068
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KEYWORD
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nonn,hard,nice
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AUTHOR
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njas
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EXTENSIONS
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Lower bounds for a(13) onwards are 9, 10, 12, 15, 15, 18, 19, 23.
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