Data related to no-3-in-line problem

[David Wilson]

The columns in

http://wwwhomes.uni-bielefeld.de/achim/no3in/table_old.txt

all refer to counts of no-3-in-line configurations on the nxn grid with various symmetries.  The columns are:

n:  Side of grid.  A00027.

all:  All configurations.  A000755.  Adds initial and final elements.

.:  Assymetric.  A037185.  Adds no new data.

/:  Diagonal symmetry.  Same as A037186.  Adds no new data.

-:  Horizontal axis symmetry.  Cannot identify in OEIS.

::  180-degree symmetry.  Same as A037187.  Adds no new data.

x:  Bidiagonal symmetry.  Same as A037188.  Adds final elements.

o:  Not sure of symmetry.  Same as A047840.  Disagrees in initial terms and adds final elements.  The disagreements may stem from table elements considered as counted in other columns.

+:  Horizontal and vertical axis symmetry.  All elements are zero.

*:  Not sure of symmetry.  Cannot identify in OEIS.

sum:  All configuration up to rotation and reflection:  Same as A000769.  Adds no new data.  
  ----- Original Message ----- 
  From: Paul D. Hanna 
  To: seqfan at ext.jussieu.fr 
  Sent: Thursday, May 12, 2005 1:08 AM
  Subject: Re: Data related to no-3-in-line problem


  Also, the link that David referrenced gives the table:
  http://wwwhomes.uni-bielefeld.de/achim/no3in/table_old.txt
   
  which extends sequence A000755 by 4 terms to be: 
   
  1,2,11,32,50,132,380,368,1135,1120,4348,3622,10568
   
  over the current:  
  http://www.research.att.com/projects/OEIS?Anum=A000755
  Sequence:  1,2,11,32,50,132,380,368,1135
  Name:      No-3-in-line problem on n X n grid.

  -- Paul

  On Thu, 12 May 2005 01:03:44 -0400 Gerald McGarvey <Gerald.McGarvey at comcast.net> writes:

    For the convenience of those interested in this problem:
    Related entry A000769 has links to other related sequences and articles including this one

No-3-in-line problem: number of ways of placing 2n points on n X n
grid so no 3 are in a line.
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000769
      Gerald 

    At 11:49 PM 5/11/2005, David Wilson wrote:

      Off of this page

      http://wwwhomes.uni-bielefeld.de/achim/no3in/readme.html

      there seems to be a lot of data on the no-3-in-line problem on the n x n grid.  Probably potential for many new seqences and extensions of existing sequences if I knew how to interpret the data.

      - David W. Wilson
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