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.
1, 2, 5, 18, 94, 709, 7710, 120882, 2732104, 89015152, 4180822859, 283067837700, 27628050712667, 3887236104777699, 788428930992492718, 230523466443694083587, 97162501670167108808501, 59035492675117768533460333, 51708108674446390274283614578, 65288256486029805607741923173692
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Keywords
Examples
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.
Links
- Code Golf Stack Exchange user "Bubbler", Tiling a staircase with staircases.
- Rémy Sigrist, PARI program for A335547
Programs
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PARI
See Links section.
Extensions
More terms from Rémy Sigrist, Sep 13 2020
Comments