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 1-4 of 4 results.

A361425 Maximum difficulty level (see A361424 for the definition) for tiling an n X n square with a set of integer-sided rectangles, rounded down to the nearest integer.

Original entry on oeis.org

1, 2, 8, 80, 1152, 53760
Offset: 1

Views

Author

Pontus von Brömssen, Mar 11 2023

Keywords

Comments

For all currently known terms, the maximum difficulty level is an integer.

Crossrefs

Main diagonal of A361424.
Cf. A360630, A361217, A361222.

A361426 Maximum difficulty level (see A361424 for the definition) for tiling an n X 2 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

Original entry on oeis.org

2, 2, 6, 12, 16, 48, 53, 120, 320, 280, 1120, 2240, 2986, 8960, 17920, 26880, 53760, 107520, 134400, 268800, 537600, 591360, 1182720, 2365440, 2956800, 5677056, 11354112
Offset: 1

Views

Author

Pontus von Brömssen, Mar 11 2023

Keywords

Comments

The only cases, currently known to the author, for which the maximum difficulty level is not an integer, are n = 7 (difficulty level 160/3) and n = 13 (difficulty level 8960/3).

Examples

			The following table shows all sets of pieces that give the maximum (n,2)-tiling difficulty level up to n = 27.
    \           Number of pieces of size
   n \  1X1 | 1X2 | 1X3 | 1X4 | 1X5 | 1X7 | 2X2 | 2X3
  ----+-----+-----+-----+-----+-----+-----+-----+----
   1  |  0  |  1  |  0  |  0  |  0  |  0  |  0  |  0
   2  |  0  |  2  |  0  |  0  |  0  |  0  |  0  |  0
   3  |  1  |  1  |  1  |  0  |  0  |  0  |  0  |  0
   4  |  0  |  2  |  0  |  1  |  0  |  0  |  0  |  0
   4  |  0  |  1  |  2  |  0  |  0  |  0  |  0  |  0
   5  |  1  |  2  |  0  |  0  |  1  |  0  |  0  |  0
   5  |  0  |  3  |  0  |  1  |  0  |  0  |  0  |  0
   6  |  0  |  1  |  2  |  1  |  0  |  0  |  0  |  0
   7  |  0  |  1  |  4  |  0  |  0  |  0  |  0  |  0
   8  |  2  |  0  |  2  |  1  |  0  |  0  |  1  |  0
   8  |  0  |  1  |  2  |  1  |  0  |  0  |  1  |  0
   9  |  1  |  0  |  3  |  2  |  0  |  0  |  0  |  0
  10  |  2  |  0  |  2  |  1  |  0  |  0  |  2  |  0
  11  |  1  |  0  |  3  |  2  |  0  |  0  |  1  |  0
  12  |  1  |  0  |  3  |  2  |  0  |  0  |  0  |  1
  12  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  0
  13  |  1  |  0  |  3  |  2  |  0  |  0  |  2  |  0
  14  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  0
  15  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  1
  16  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  0
  17  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  1
  18  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  2
  19  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  1
  20  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  2
  21  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  3
  22  |  0  |  0  |  5  |  2  |  0  |  1  |  2  |  1
  22  |  0  |  0  |  5  |  0  |  3  |  0  |  2  |  1
  22  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  2
  23  |  0  |  0  |  5  |  2  |  0  |  1  |  1  |  2
  23  |  0  |  0  |  5  |  0  |  3  |  0  |  1  |  2
  23  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  3
  24  |  0  |  0  |  5  |  2  |  0  |  1  |  0  |  3
  24  |  0  |  0  |  5  |  0  |  3  |  0  |  0  |  3
  24  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  4
  25  |  0  |  0  |  3  |  4  |  0  |  1  |  0  |  3
  26  |  0  |  0  |  5  |  2  |  0  |  1  |  1  |  3
  26  |  0  |  0  |  5  |  0  |  3  |  0  |  1  |  3
  27  |  0  |  0  |  5  |  2  |  0  |  1  |  0  |  4
  27  |  0  |  0  |  5  |  0  |  3  |  0  |  0  |  4

Crossrefs

Second column of A361424.
Cf. A360631, A361218, A361224.

A361427 Maximum difficulty level (see A361424 for the definition) for tiling an n X 3 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

Original entry on oeis.org

2, 6, 8, 48, 80, 480, 960, 1920, 3360, 13440, 20160, 60480, 80640, 201600, 967680, 1612800
Offset: 1

Views

Author

Pontus von Brömssen, Mar 11 2023

Keywords

Comments

For all currently known terms, the maximum difficulty level is an integer.

Examples

			The following table shows all sets of pieces that give the maximum (n,3)-tiling difficulty level up to n = 16.
    \               Number of pieces of size
   n \ 1X1|1X2|1X3|1X4|1X5|1X6|1X7|1X8|1X9|1X10|1X12|2X2|2X3|2X4|2X5
  ----+---+---+---+---+---+---+---+---+---+----+----+---+---+---+---
   1  | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   1  | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   2  | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   3  | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   4  | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   5  | 0 | 3 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   5  | 0 | 1 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   6  | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   7  | 0 | 3 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   7  | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 0
   8  | 0 | 3 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 0
   9  | 4 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 1 | 0 | 0
   9  | 2 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 1 | 0 | 0
   9  | 0 | 4 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   9  | 0 | 3 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0  | 0  | 2 | 0 | 0 | 0
  10  | 3 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 1
  11  | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 1  | 0  | 0 | 1 | 0 | 0
  12  | 3 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0  | 0  | 2 | 0 | 0 | 1
  13  | 1 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 1 | 1
  13  | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 1  | 1 | 1 | 0 | 0
  14  | 4 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 0 | 2 | 0
  14  | 3 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 0  | 0  | 3 | 0 | 0 | 1
  14  | 2 | 0 | 0 | 2 | 4 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 1 | 0
  15  | 1 | 0 | 0 | 3 | 2 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 1
  16  | 3 | 0 | 0 | 2 | 1 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 2 | 1

Crossrefs

Third column of A361424.
Cf. A360632, A361219, A361225.

A361428 Maximum difficulty level (see A361424 for the definition) for tiling an n X 4 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

Original entry on oeis.org

4, 12, 48, 80, 480, 2880, 13440, 53760, 107520, 322560, 725760
Offset: 1

Views

Author

Pontus von Brömssen, Mar 11 2023

Keywords

Comments

For all currently known terms, the maximum difficulty level is an integer.

Examples

			The following table shows all sets of pieces that give the maximum (n,4)-tiling difficulty level up to n = 11.
    \                       Number of pieces of size
   n \  1X1 | 1X2 | 1X3 | 1X4 | 1X5 | 1X6 | 1X7 | 1X8 | 1X10| 2X2 | 2X3 | 2X4
  ----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----
   1  |  0  |  2  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   2  |  0  |  2  |  0  |  1  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   2  |  0  |  1  |  2  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   3  |  0  |  1  |  2  |  1  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   4  |  0  |  1  |  2  |  2  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   5  |  0  |  1  |  3  |  1  |  1  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   6  |  0  |  1  |  1  |  1  |  1  |  1  |  0  |  0  |  0  |  1  |  0  |  0
   6  |  0  |  0  |  2  |  2  |  2  |  0  |  0  |  0  |  0  |  0  |  0  |  0
   7  |  0  |  3  |  0  |  0  |  2  |  1  |  0  |  0  |  0  |  0  |  1  |  0
   7  |  0  |  0  |  3  |  2  |  1  |  1  |  0  |  0  |  0  |  0  |  0  |  0
   8  |  0  |  3  |  0  |  0  |  1  |  1  |  1  |  0  |  0  |  2  |  0  |  0
   9  |  0  |  3  |  0  |  0  |  1  |  0  |  1  |  1  |  0  |  1  |  1  |  0
   9  |  0  |  3  |  0  |  0  |  0  |  2  |  0  |  1  |  0  |  1  |  1  |  0
   9  |  0  |  0  |  3  |  1  |  2  |  1  |  1  |  0  |  0  |  0  |  0  |  0
  10  |  0  |  2  |  0  |  0  |  1  |  1  |  1  |  0  |  0  |  1  |  1  |  1
  11  |  1  |  2  |  0  |  0  |  0  |  0  |  1  |  2  |  0  |  1  |  2  |  0
  11  |  1  |  1  |  0  |  0  |  1  |  2  |  0  |  0  |  1  |  2  |  1  |  0

Crossrefs

Fourth column of A361424.
Cf. A361220.
Showing 1-4 of 4 results.

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

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