login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A342430 Number of prime polyominoes with n cells. 0
0, 1, 1, 2, 1, 12, 5, 108, 145, 974, 2210, 17073, 31950, 238591 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

We say that a free polyomino is prime if it cannot be tiled by any other free polyomino besides the 1x1 square and itself.

The tiling of P must be with a single polyomino, and that single polyomino may not be the unique monomino or P itself. For example, decomposing the T-tetromino into a 3x1 and a 1x1 would use multiple tiles, and this is not permitted.

It can be shown that a(n) > 0 for all n >= 4, by considering the polyomino whose cells are at (0,1), (-1,1), (0,2), and (x,0) for all x = 0, 1, ..., n-4.

LINKS

Table of n, a(n) for n=0..13.

Cibulis, Liu, and Wainwright, Polyomino Number Theory (I), Crux Mathematicorum, 28(3) (2002), 147-150.

FORMULA

a(n) = A000105(n) if n is prime.

EXAMPLE

For n = 4, the T-tetromino cannot be decomposed into smaller congruent polyominoes:

      +---+

      |   |

  +---+   +---+

  |           |

  +-----------+

The other four free tetrominoes can, however:

  +---+

  |   |

  |   |    +---+

  |   |    |   |

  +---+    |   |         +---+---+        +---+---+

  |   |    |   |         |   |   |        |       |

  |   |    +---+---+     |   |   |    +---+---+---+

  |   |    |       |     |   |   |    |       |

  +---+    +-------+     +---+---+    +---+---+

Thus a(4) = 1.

CROSSREFS

Cf. A000105, A125759, A213376.

Sequence in context: A107722 A167128 A332749 * A181417 A048743 A049055

Adjacent sequences:  A342427 A342428 A342429 * A342431 A342432 A342433

KEYWORD

nonn,hard,more,nice

AUTHOR

Drake Thomas, Mar 11 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)