A364457
Number A(n,k) of tilings of a k X n rectangle using dominoes 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, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 6, 6, 1, 1, 1, 2, 17, 30, 17, 2, 1, 1, 2, 43, 145, 145, 43, 2, 1, 1, 3, 108, 733, 1352, 733, 108, 3, 1, 1, 4, 280, 3540, 12688, 12688, 3540, 280, 4, 1, 1, 5, 727, 17300, 115958, 226922, 115958, 17300, 727, 5, 1
Offset: 0
A(3,2) = A(2,3) = 6:
.___. .___. .___. .___. .___. .___.
| | | |___| | | | |___| | ._| |_. |
| | | |___| |_|_| | | | |_| | | |_|
|_|_| |___| |___| |_|_| |___| |___| .
.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 0, 1, 1, 1, 2, 2, 3, ...
1, 1, 2, 6, 17, 43, 108, 280, ...
1, 1, 6, 30, 145, 733, 3540, 17300, ...
1, 1, 17, 145, 1352, 12688, 115958, 1075397, ...
1, 2, 43, 733, 12688, 226922, 3927233, 68846551, ...
1, 2, 108, 3540, 115958, 3927233, 128441094, 4263997124, ...
1, 3, 280, 17300, 1075397, 68846551, 4263997124, 267855152858, ...
Columns (or rows) k=0-10 give:
A000012,
A182097(n) =
A000931(n+3),
A019439,
A364460,
A364155,
A364556,
A364616,
A364617,
A364632,
A364638,
A364640.
A219994
Number of tilings of an n X n square using dominoes and right trominoes.
Original entry on oeis.org
1, 0, 2, 8, 380, 21272, 5350806, 3238675344, 6652506271144, 38896105985522272, 711716770252031164458, 38776997923112110535353528, 6460929292946758939597712150496, 3245656750963660788826395580466708824, 4953412325525289651086730443567098343730966, 22873302288206466754758793232467436030071524731072
Offset: 0
a(3) = 8, because there are 8 tilings of a 3 X 3 square using dominoes and right trominoes:
.___._. .___._. .___._. .___._.
|___| | |___| | |___| | |_. | |
| ._|_| | | |_| | |___| | |_|_|
|_|___| |_|___| |_|___| |_|___|
._.___. ._.___. ._.___. ._.___.
| |___| | | ._| | |___| | |___|
|___| | |_|_| | |_|_. | |_| | |
|___|_| |___|_| |___|_| |___|_| .
A219874
Number of tilings of an n X n square using dominoes and straight (3 X 1) trominoes.
Original entry on oeis.org
1, 0, 2, 14, 184, 9612, 1143834, 354859954, 295743829064, 631206895803116, 3541054185616706122, 51821077154605344550820, 1976225122734369352127065686, 196913655491597719598898811003348, 51179690353659852099434654264900753288, 34716223657627061096793572212632925410608268
Offset: 0
a(3) = 14, because there are 14 tilings of a 3 X 3 square using dominoes and straight (3 X 1) trominoes:
._____. ._____. ._____. ._____. .___._. .___._. .___._.
| | | | | | | | | |___| | |___| | | | | |___| | |___| |
| | | | | |_|_| | |___| | | | | |_|_| | |___| | | | | |
|_|_|_| |_|___| |_|___| |_|_|_| |___|_| |___|_| |_|_|_|
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_____| |_____| |_____| |_____| | |___| | | | | |___| |
|_____| | |___| | | | | |___| | |_|___| |_|_|_| |___|_|
|_____| |_|___| |_|_|_| |___|_| |_____| |_____| |_____| .
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