A270061
Number A(n,k) of tilings of a k X n rectangle using monominoes and trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 3, 14, 14, 3, 1, 1, 4, 45, 93, 45, 4, 1, 1, 6, 140, 590, 590, 140, 6, 1, 1, 9, 438, 3710, 7517, 3710, 438, 9, 1, 1, 13, 1371, 23509, 96176, 96176, 23509, 1371, 13, 1, 1, 19, 4287, 148796, 1238818, 2501946, 1238818, 148796, 4287, 19, 1
Offset: 0
A(2,3) = A(3,2) = 14:
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_|
|_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_|
.
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. |
|_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| .
.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 2, 3, 4, 6, ...
1, 1, 5, 14, 45, 140, 438, ...
1, 2, 14, 93, 590, 3710, 23509, ...
1, 3, 45, 590, 7517, 96176, 1238818, ...
1, 4, 140, 3710, 96176, 2501946, 65410388, ...
1, 6, 438, 23509, 1238818, 65410388, 3473827027, ...
Columns (or rows) k=0-10 give:
A000012,
A000930,
A270062,
A270063,
A270064,
A270065,
A270066,
A270067,
A270068,
A270069,
A270070.
A353777
Number of tilings of an n X n square using dominoes, monominoes and 2 X 2 tiles.
Original entry on oeis.org
1, 1, 8, 163, 15623, 5684228, 8459468955, 50280716999785, 1202536689448371122, 115462301811597894998929, 44537596159273736617786474211, 69003082378039459280864860681919942, 429429579883061866326542598342441907826951, 10734684843612889640707750537898705644071715970757
Offset: 0
a(2) = 8:
.___. .___. .___. .___. .___. .___. .___. .___.
| | |_|_| |___| | | | |_|_| |___| |_| | | |_|
|___| |_|_| |___| |_|_| |___| |_|_| |_|_| |_|_| .
A353934
Number of tilings of an n X n square using right trominoes, dominoes, and monominoes.
Original entry on oeis.org
1, 1, 11, 369, 83374, 90916452, 546063639624, 17259079054003609, 2916019543694306398589, 2620143594924539083433405392, 12541344781693990981151732534871036, 319608708168951734031266758322647453517098, 43373075269161087186367095378869660507262626652634
Offset: 0
a(2) = 11:
.___. .___. .___. .___. .___. .___. .___. .___. .___. .___. .___.
|_|_| |___| | | | |_|_| |___| |_| | | |_| |_| | |_. | | ._| | |_|
|_|_| |___| |_|_| |___| |_|_| |_|_| |_|_| |___| |_|_| |_|_| |___| .
Cf.
A004003,
A028420,
A063443,
A219874,
A219952,
A219994,
A220061,
A220778,
A233807,
A270071,
A353777.
Showing 1-3 of 3 results.