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a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes.
1

%I #31 Oct 04 2020 02:44:56

%S 1,2,8,57,806,20840,1038266,97115638,17213517207,5768580741287

%N a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes.

%C A size-n staircase polynomo is a polyomino consisting of n left-aligned rows in increasing length of 1, 2, ..., n. Rotations of staircase polyominoes are also polyominoes.

%H Code Golf Stack Exchange user "Bubbler", <a href="https://codegolf.stackexchange.com/q/210748/53884">Tiling a staircase with staircases</a>.

%e For n = 3 the a(3) = 8 tilings are:

%e +---+ +---+ +---+ +---+

%e | | | | | | | |

%e +---+---+ + +---+ +---+---+ +---+---+

%e | | | | | | | | | | |

%e +---+---+---+, +---+---+---+, + +---+---+, +---+ +---+,

%e | | | | | | | | | | | | | |

%e +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+

%e +---+ +---+ +---+ +---+

%e | | | | | | | |

%e +---+---+ +---+---+ +---+---+ + +---+

%e | | | | | | | | |

%e +---+ +---+, + +---+---+, +---+ +---+, + +---+.

%e | | | | | | | | | | | | |

%e +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+

%Y Cf. A000105, A045846, A219924, A254414, A335547.

%K nonn,more

%O 1,2

%A _Peter Kagey_, Sep 08 2020

%E a(8) from _Seiichi Manyama_, Sep 09 2020

%E a(9)-a(10) from _Bert Dobbelaere_, Sep 12 2020