

A172992


Maximal number of 4tree rows in ntree orchard problem in which the tree coordinates are integers.


2



0, 0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 7, 9, 10, 12, 14, 15, 17, 20, 23, 24, 26, 28, 30, 32, 34, 36, 39, 41, 44, 46, 48, 50, 52, 54, 57, 59, 62, 64, 67, 69, 72, 75, 78, 80, 83, 86, 89, 91, 94, 97, 100, 103, 106, 109, 112, 116, 120, 123, 126
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OFFSET

1,7


COMMENTS

At the end of 2011 there was a 3month programming competition (http://infinitesearchspace.dyndns.org/orchardplanting) for this problem for n in the range [11,60]. Later there was an unofficial contest (http://infinitesearchspace.dyndns.org/content/orchardminicontest) for finding optimal solutions that can be placed on the smallest possible grids.
The terms in this sequences are the best known solutions to date and they may not be optimal.
Any solution that can be represented with integer coordinates can also be represented with realvalued coordinates, hence A172992(n)<=A006065(n). It is believed (but not proved) that some realvalued solutions cannot be represented by integervalued solutions. For example A172992(16)=14, but A006065(16)=15. (End)


LINKS



EXAMPLE

It is possible to place 10 points on an integer grid such that there are 5 straight lines with exactly 4 points lying on each line. Hence a(10) is 5.  Dmitry Kamenetsky, Feb 23 2012 (see the illustration by Hugo Pfoertner!)


CROSSREFS

A006065 is the same problem, but with realvalued tree coordinates.


KEYWORD

hard,nonn


AUTHOR



EXTENSIONS



STATUS

approved



