A353878
Number of tilings of a 3 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.
Original entry on oeis.org
1, 3, 44, 369, 3633, 34002, 323293, 3058623, 28982628, 274494621, 2600148629, 24628666626, 233286962601, 2209723174731, 20930806288252, 198259418947833, 1877940242218857, 17788105074906162, 168491350295593637, 1595972975308532199, 15117273008425964916
Offset: 0
a(2)=44
The number of tilings (mirroring included) using r trominoes
___ ___ ___
r=1: | _| | |_| r=2: | _| r=0: 22 = A030186(3)
|_|3| |___| |_| |
|___| |_2_| |___|
4*3 + 4*2 + 2*1 + 22 = 44
Legend:
___ ___ ___
|_2_| stands for |___| or |_|_|
_ _ _ _
_|3| _| | _|_| _|_|
|___| stands for |_|_| or |___| or |_|_|
A353879
Number of tilings of a 4 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.
Original entry on oeis.org
1, 5, 189, 3633, 83374, 1817897, 40220893, 886130549, 19546906987, 431024540644, 9505433227293, 209617856008535, 4622624792880217, 101940750143038657, 2248057208102711472, 49575464007447758483, 1093267021618939507743, 24109360928450426884813, 531673668551361276666101
Offset: 0
a(2)=189.
The number of tilings (mirroring included) using r trominoes
___ ___ ___ ___
r=1: | _| | _| | |_| |_2_| r=0: 71 = A030186(4)
|_|_| |_| | |___| |_ |
| 7 | |3|_| | 7 | |3|_|
|___| |___| |___| |___|
4*7 + 4*3 + 4*7 + 4*6 = 92
___ ___ ___ ___ ___ ___ ___
r=2: | _| | _| | _| | _| | _| | |_| | |_|
|_| | |_|2| |_|_| |_|_| |_|_| |___| |___|
|___| | |_| | _|_|_| | |_ | |_ | | _|
|_2_| |___| |_|_| |___| |_|_| |_|_| |_|_|
4*2 + 2*2 + 4*1 + 2*1 + 4*1 + 2*1 + 2*1 = 26
Result: a(2) = 71+92+26 = 189.
Legend:
___ ___ ___
|_2_| stands for |___| or |_|_|
_ _ _ _
_|3| _| | _|_| _|_|
|___| stands for |_|_| or |___| or |_|_|
___ ___ ___ ___ ___ ___ ___ ___
| 7 | |___| |_|_| |___| | | | |_| | | |_| |_|_|
|___| stands for |___|,|___|,|_|_|,|_|_|,|_|_|,|_|_| or |_|_|
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.
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