%I A006065 M0290
%S A006065 0,0,0,1,1,1,2,2,3,5,6,7,9,10,12,15,16,18
%N A006065 Maximal number of 4-tree rows in n-tree orchard problem.
%C A006065 Maximum number of rows with exactly 4 trees in each row if there are 
               n trees in the orchard.
%C A006065 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. - N. J. A. Sloane (njas(AT)research.att.com), May 
               13 2008
%D A006065 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006065 S. A. Burr, B. Gr\"{u}nbaum and N. J. A. Sloane, The Orchard Problem, 
               Geometriae Dedicata, 2 (1974), 397-424.
%D A006065 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, Chap. 22.
%D A006065 Xianzu Lin, A new result about orchard-planting problem, Preprint, 2005. 
               [Shows a(20) >= 23.]
%H A006065 P. Berloquin, <a href="a008997.jpg">a(12) >= 7</a> (from an article in 
               Jeux & Strategies from 1983 - see Fig. 10)
%H A006065 S. A. Burr, B. Gr\"{u}nbaum and N. J. A. Sloane, <a href="http://www.research.att.com/
               ~njas/doc/ORCHARD/orchard.html">The Orchard Problem</a>, Geometriae 
               Dedicata, 2 (1974), 397-424.
%H A006065 Du, Zhao Hui, <a href="http://bbs.emath.ac.cn/viewthread.php?tid=703&page=11#pid9076">
               Code to verify a(13) to a(16) for orchard planting problem</a>
%H A006065 Xianzu Lin, <a href="a006065.gif">Illustration showing that a(20) >= 
               23</a> [The points S and T are at infinity]
%H A006065 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006065 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A006065 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Orchard-PlantingProblem.html">Link to a section of The World of Mathematics.</
               a>
%H A006065 <a href="http://zdu.spaces.live.com/blog/cns!C95152CB25EF2037!122.entry">
               Link to one of the optimal results from 13~17 trees</a> [From Du, 
               Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 11 2008]
%Y A006065 Cf. A003035, A008997.
%Y A006065 Sequence in context: A098382 A098180 A117752 this_sequence A096981 A035541 
               A060966
%Y A006065 Adjacent sequences: A006062 A006063 A006064 this_sequence A006066 A006067 
               A006068
%K A006065 nonn,hard,nice
%O A006065 1,7
%A A006065 N. J. A. Sloane (njas(AT)research.att.com).
%E A006065 a(13) - a(15) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Aug 24 2008
%E A006065 a(17) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 11 2008
%E A006065 a(18) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 25 2008