|
|
A233320
|
|
Number A(n,k) of tilings of a k X n rectangle using trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
|
|
17
|
|
|
1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 3, 3, 0, 1, 1, 0, 0, 10, 0, 0, 1, 1, 1, 0, 23, 23, 0, 1, 1, 1, 0, 11, 62, 0, 62, 11, 0, 1, 1, 0, 0, 170, 0, 0, 170, 0, 0, 1, 1, 1, 0, 441, 939, 0, 939, 441, 0, 1, 1, 1, 0, 41, 1173, 0, 8342, 8342, 0, 1173, 41, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,18
|
|
COMMENTS
|
Every row and column satisfies a linear recurrence. - Peter Kagey, Jul 17 2019
|
|
LINKS
|
|
|
FORMULA
|
A(n,k) = 0 <=> n*k mod 3 > 0.
|
|
EXAMPLE
|
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 0, 0, 1, 0, 0, 1, ...
1, 0, 0, 3, 0, 0, 11, ...
1, 1, 3, 10, 23, 62, 170, ...
1, 0, 0, 23, 0, 0, 939, ...
1, 0, 0, 62, 0, 0, 8342, ...
1, 1, 11, 170, 939, 8342, 80092, ...
1, 0, 0, 441, 0, 0, 614581, ...
1, 0, 0, 1173, 0, 0, 5271923, ...
|
|
CROSSREFS
|
Columns (or rows) include: A000012, A001835, A134438, A233339, A233340, A233290, A233343, A269958, A215826, A269959, A269664.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|