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A335547 a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes in the same direction as the size n staircase polyomino. 4
1, 2, 5, 18, 94, 709, 7710, 120882, 2732104, 89015152, 4180822859, 283067837700, 27628050712667, 3887236104777699, 788428930992492718, 230523466443694083587, 97162501670167108808501, 59035492675117768533460333, 51708108674446390274283614578, 65288256486029805607741923173692 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A size-n staircase polynomo is a polyomino consisting of n left-aligned rows in increasing length of 1, 2, ..., n.

LINKS

Table of n, a(n) for n=1..20.

Code Golf Stack Exchange user "Bubbler", Tiling a staircase with staircases.

Rémy Sigrist, PARI program for A335547

EXAMPLE

For n = 3 the a(3) = 5 tilings are:

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

|   |          |   |          |   |          |   |

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

|   |   |      |       |      |   |   |      |   |   |

+---+---+---+, +---+---+---+, +   +---+---+, +---+   +---+,

|   |   |   |  |   |   |   |  |       |   |  |   |       |

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

+---+

|   |

+   +---+

|       |

+       +---+.

|           |

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

For n = 4 the a(4) = 5+5+3+3+2 = 18 tilings are:

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

|   |              |   |              |   |

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

|   |   |          |   |   |          |   |   |

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

|   |   |   |      |   |   |   |      |   |   |   |

+---+---+---+---+, +   +---+---+---+, +---+   +---+---+,

|   |   |   |   |  |       |   |   |  |   |       |   |

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

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

|   |              |   |              |   |

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

|   |   |          |   |   |          |       |

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

|   |   |   |      |   |   |   |      |   |   |   |

+---+---+   +---+, +   +---+   +---+, +---+---+---+---+,

|   |   |       |  |       |       |  |   |   |   |   |

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

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

|   |              |   |              |   |

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

|       |          |       |          |       |

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

|   |   |   |      |   |   |   |      |   |   |   |

+   +---+---+---+, +---+   +---+---+, +---+---+   +---+,

|       |   |   |  |   |       |   |  |   |   |       |

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

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

|   |              |   |              |   |

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

|       |          |   |   |          |   |   |

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

|   |   |   |      |       |   |      |       |   |

+   +---+   +---+, +---+---+---+---+, +       +---+---+,

|       |       |  |   |   |   |   |  |           |   |

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

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

|   |              |   |              |   |

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

|   |   |          |   |   |          |   |   |

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

|       |   |      |   |       |      |   |       |

+---+---+   +---+, +---+---+---+---+, +   +---+---+---+,

|   |   |       |  |   |   |   |   |  |       |   |   |

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

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

|   |              |   |              |   |

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

|   |   |          |       |          |       |

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

|   |       |      |           |      |           |

+---+       +---+, +---+---+---+---+, +           +---+.

|   |           |  |   |   |   |   |  |               |

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

a(5) = 8+5+5+5+3+8+5+5+5+3+8+3+5+8+5+3+8+2 = 94.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A334617, A335967, A336479.

Sequence in context: A217389 A123310 A058119 * A075441 A187008 A333837

Adjacent sequences:  A335544 A335545 A335546 * A335548 A335549 A335550

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 12 2020

EXTENSIONS

More terms from Rémy Sigrist, Sep 13 2020

STATUS

approved

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)