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 1-3 of 3 results.

A226980 Number of ways to cut an n X n square into squares with integer sides, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 4 elements.

Original entry on oeis.org

0, 0, 1, 6, 26, 264, 1157, 23460, 153485, 6748424, 70521609, 6791578258
Offset: 1

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Author

Keywords

Examples

			For n=5, there are 26 dissections where the orbits under the symmetry group of the square, D4, have 4 elements.
The 6 dissections for n=4 can be seen in A240123 and A240125.
		

Crossrefs

Formula

A226978(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).
1*A226978(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).
A226980(n) = A240123(n) + A240124(n) + A240125(n).

Extensions

a(8)-a(12) from Ed Wynn, Apr 01 2014

A240123 Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has a reflective symmetry in one diagonal, but no other symmetries.

Original entry on oeis.org

0, 0, 1, 3, 19, 107, 847, 8647, 119835, 2255123, 58125783, 2050662011
Offset: 1

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Author

Ed Wynn, Apr 01 2014

Keywords

Comments

'Inequivalent' has the same sense as in A224239: we do not regard dissections that differ by a rotation and/or reflection as distinct.

Examples

			The three dissections for n=4:
---------    ---------    ---------
|   | | |    |   |   |    |     | |
|   -----    |   |   |    |     ---
|   | | |    |   |   |    |     | |
---------    ---------    |     ---
| | | | |    |   | | |    |     | |
---------    |   -----    ---------
| | | | |    |   | | |    | | | | |
---------    ---------    ---------
		

Crossrefs

A240124 Number of inequivalent ways to cut an n X n square into squares with integer sides, such that the dissection has 180-degree rotational symmetry, but no other symmetries.

Original entry on oeis.org

0, 0, 0, 0, 2, 19, 109, 1781, 13660, 397689, 5368943, 289864745
Offset: 1

Views

Author

Ed Wynn, Apr 01 2014

Keywords

Examples

			The two dissections for n=5:
-----------    -----------
|   |   | |    | |   | | |
|   |   ---    ---   -----
|   |   | |    | |   | | |
-----------    -----------
| | | | | |    | | | | | |
-----------    -----------
| |   |   |    | | |   | |
---   |   |    -----   ---
| |   |   |    | | |   | |
-----------    -----------
		

Crossrefs

Showing 1-3 of 3 results.