OFFSET

1,10

COMMENTS

All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 2 X 3 rectangle can only be used once, regardless of whether it lies horizontally or vertically.

EXAMPLE

a(2), a(3), a(5), a(7), a(11) = 1 as the only possible tiling is that using an n X n square where n is a prime number. It is likely 11 is the last prime indexed term that equals 1 although this is unknown.

a(10) = 4128. And example tiling is:

.

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

| | | |

+ + + +

| | | |

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

| | |

+ + +

| | |

+ + +

| | |

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

| | |

+ + +

| | |

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

| | |

+ + +

| | |

+ + +

| | |

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

.

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon, Mar 10 2023

STATUS

approved