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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
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
Code Golf Stack Exchange user "Bubbler", Tiling a staircase with staircases.
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 12 2020
EXTENSIONS
More terms from Rémy Sigrist, Sep 13 2020
STATUS
approved