1,7

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. - N. J. A. Sloane (njas(AT)research.att.com), May 13 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.]

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]

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.

Link to one of the optimal results from 13~17 trees [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 11 2008]

Cf. A003035, A008997.

Sequence in context: A098382 A098180 A117752 this_sequence A096981 A035541 A060966

Adjacent sequences: A006062 A006063 A006064 this_sequence A006066 A006067 A006068

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).

a(13) - a(15) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Aug 24 2008

a(17) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 11 2008

a(18) from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Nov 25 2008