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 1-5 of 5 results.

A234351 Number of non-equivalent (mod D_3) ways to arrange 3 indistinguishable points on a triangular grid of side n so that no three points are collinear.

Original entry on oeis.org

1, 5, 22, 77, 217, 530, 1149, 2288, 4231, 7400, 12322, 19725, 30486, 45768, 66917, 95669
Offset: 2

Views

Author

Heinrich Ludwig, Dec 30 2013

Keywords

Comments

Column 3 of triangle A234350.
Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194131.

Examples

			There are a(3) = 5 non-equivalent ways to arrange 3 indistinguishable points (x) on a triangular grid of side 3:
     x         .         x         x         x
    . .       x x       x x       . .       x .
   x . x     . x .     . . .     . x x     . x .

Crossrefs

Cf. A234350, A194131
Arranging 4 points: A234352
Arranging 5 points: A234353
Arranging 6 points: A234354

Extensions

a(14)-a(17) from Heinrich Ludwig, Apr 19 2016

A234352 Number of non-equivalent (mod D_3) ways to arrange 4 indistinguishable points on a triangular grid of side n so that no three points are collinear.

Original entry on oeis.org

2, 24, 153, 713, 2557, 7661, 20055, 47153, 101821, 205322, 390580, 707708, 1229969, 2060777, 3344487
Offset: 3

Views

Author

Heinrich Ludwig, Dec 30 2013

Keywords

Comments

Column 4 of triangle A234350.
Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194132.

Examples

			There are a(3) = 2 non-equivalent ways to arrange 4 indistinguishable points (x) on a triangular grid of side 3:
    x         .
   x x       x x
  . x .     x . x

Crossrefs

Cf. A234350, A194132
Arranging 3 points: A234351
Arranging 5 points: A234353
Arranging 6 points: A234354

Extensions

a(14)-a(17) from Heinrich Ludwig, Apr 19 2016

A234353 Number of non-equivalent (mod D_3) ways to arrange 5 indistinguishable points on a triangular grid of side n so that no three points are collinear.

Original entry on oeis.org

8, 140, 1290, 7374, 32477, 116420, 358112, 976063, 2425756, 5560046, 11946923, 24274195, 46975815, 87140153
Offset: 4

Views

Author

Heinrich Ludwig, Dec 30 2013

Keywords

Comments

Column 5 of triangle A234350.
Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194133.

Examples

			There are a(4) = 8 non-equivalent ways to arrange 5 indistinguishable points (x) on a triangular grid of side 4. Some examples:
      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. A234350, A194133
Arranging 3 points: A234351
Arranging 4 points: A234352
Arranging 6 points: A234354

Extensions

a(14)-a(17) from Heinrich Ludwig, Apr 19 2016

A234354 Number of non-equivalent (mod D_3) ways to arrange 6 indistinguishable points on a triangular grid of side n so that no three points are collinear.

Original entry on oeis.org

1, 47, 1112, 11743, 82988, 433372, 1820163, 6459496, 20287372, 57129426, 147915285, 356109110, 804785159, 1722171831
Offset: 4

Views

Author

Heinrich Ludwig, Dec 30 2013

Keywords

Comments

Column 6 of triangle A234350.
Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194134.

Examples

			There is a(4) = 1 non-equivalent way to arrange 6 indistinguishable points (x) on a triangular grid of side 4:
     .
    x x
   x . x
  . x x .

Crossrefs

Cf. A234350, A194134
Arranging 3 points: A234351
Arranging 4 points: A234352
Arranging 5 points: A234353

Extensions

a(14)-a(17) from Heinrich Ludwig, Apr 19 2016

A234349 Maximal number of points that can be placed on a triangular grid of side n so that no three points are collinear.

Original entry on oeis.org

1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 25, 27, 28
Offset: 1

Views

Author

Heinrich Ludwig, Dec 24 2013

Keywords

Comments

Length of the n-th row in triangle A194136 and triangle A234350.
Differs from A007401 first at n=14.

Examples

			In a triangular grid of side 5 at most 7 points (x) can be placed so that no three of them are on a straight line. (There are exactly 2 ways to do it, rotations and reflections ignored.)
        .              x
       . x            . .
      x . x          x . x
     x . x .        . x x .
    . x . x .      . x . x .

Crossrefs

Cf. A194136, A234350.

Extensions

a(13)-a(14) from Heinrich Ludwig, Jan 10 2014
a(15)-a(16) from Heinrich Ludwig, Jan 28 2014
a(17)-a(21) from Rob Pratt, Jul 27 2015
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.