cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A296468 Largest number of points that can be placed on an n X n point grid so that no point is equally distant from two other points on the same row or column.

Original entry on oeis.org

1, 4, 6, 11, 17, 24, 28, 32, 40, 47, 57, 66, 78, 90
Offset: 1

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Author

Heinrich Ludwig, Dec 13 2017

Keywords

Comments

This sequence is a 2-dimensional generalization of A003002 ("no 3-term arithmetic progressions").

Examples

			Up to 66 points (x) may be placed on a 12 X 12 point grid. Example with two symmetry axes:
x x . x x . . . . x x .
x . x . . x x . . x . x
. x x . . . . x x . x x
x . . . . x x . x x . .
x . . . x . x x . x . .
. x . x . . . x x . x .
. x . x x . . . x . x .
. . x . x x . x . . . x
. . x x . x x . . . . x
x x . x x . . . . x x .
x . x . . x x . . x . x
. x x . . . . x x . x x

Crossrefs

Cf. A003002, A193838, A300131.

Extensions

a(13)-a(14) from Bert Dobbelaere, Jan 06 2020

A296994 Largest number of points that can be selected from an n X n X n triangular point grid so that no selected point is equally distant from two other selected points on a straight line, which is parallel to one side of the grid.

Original entry on oeis.org

1, 3, 4, 7, 10, 14, 18, 20, 23, 27, 31, 36, 42, 48, 54, 61, 68, 76, 84, 92, 98
Offset: 1

Views

Author

Heinrich Ludwig, Mar 26 2018

Keywords

Comments

This sequence generalizes the idea of A003002 ("no 3-term arithmetic progressions") for triangular point grids.
For the same idea applied to square grids see A296468 and A300131.

Examples

			At most 54 points (X) can be chosen from a 15 X 15 X 15 triangular point grid under the condition mentioned above. Example:
                 o
                X X
               X o X
              o X X o
             X X o X X
            X o o o o X
           o o X o X o o
          o o o o o o o o
         o o X X o X X o o
        o X o o X X o o X o
       X X o o X o X o o X X
      X o X X o o o o X X o X
     o X X o o X o X o o X X o
    X X o X X o o o o X X o X X
   X o o o o X X o X X o o o o X

Crossrefs

Cf. A296468, A300131.

Extensions

a(20) from Heinrich Ludwig, Apr 24 2018
a(21) from Heinrich Ludwig, May 01 2018
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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