A172993 - OEIS

%I #25 Oct 30 2019 20:53:36

%S 0,0,0,1,1,1,2,2,3,5,6,9,9,11,13,15,17,18,20,23

%N Maximal number of 4-tree rows in n-tree orchard problem in which the coordinates of trees may be complex numbers.

%H Zhao Hui Du, <a href="http://bbs.emath.ac.cn/forum.php?mod=redirect&amp;goto=findpost&amp;ptid=703&amp;pid=9076&amp;fromuid=20">Orchard planting problem with 4 trees per row</a>

%e a(12)=9: Such as 12 trees in 9 rows: example for 12 trees with 9 rows: ABCD,AEFG,AHIJ,BEHK,BFIL,CEJL,CGIK,DFJK,DGHL. Let t^2+t+1=0, coordinate in projective plane: A[0:1:0], B[1:0:0], C[1:1+t:0], D[1:t:0], E(0,0), F(0,1), G(0,-t), H(1,0), I(1,1), J(1,t+1), K(1+t,0), L(-t,1).

%Y Cf. A006065.

%K hard,more,nonn

%O 1,7

%A _Zhao Hui Du_, Feb 07 2010

%E a(12) corrected by _Zhao Hui Du_, Oct 30 2019