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:
._____. ._____. ._____. ._____. .___._. .___._. .___._.
| | | | | | | | | |___| | |___| | | | | |___| | |___| |
| | | | | |_|_| | |___| | | | | |_|_| | |___| | | | | |
|_|_|_| |_|___| |_|___| |_|_|_| |___|_| |___|_| |_|_|_|
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_____| |_____| |_____| |_____| | |___| | | | | |___| |
|_____| | |___| | | | | |___| | |_|___| |_|_|_| |___|_|
|_____| |_|___| |_|_|_| |___|_| |_____| |_____| |_____| .
A220061
Number of tilings of an n X n square using right trominoes and 1 X 1 tiles.
Original entry on oeis.org
1, 1, 5, 39, 2023, 249651, 128938297, 207866584389, 1208344842789831, 23649239068131551559, 1609120545126107661426575, 375082120094104660413783094451, 301522432794951154854984388046484015, 833441700776362178606942848178200903068675, 7931715551857283775957120938092133944383839378911
Offset: 0
a(2) = 5, because there are 5 tilings of a 2 X 2 square using right trominoes and 1 X 1 tiles:
._._. ._._. .___. .___. ._._.
|_|_| | |_| | ._| |_. | |_| |
|_|_| |___| |_|_| |_|_| |___|
A219952
Number of tilings of an n X n square using right trominoes and 2 X 2 tiles.
Original entry on oeis.org
1, 0, 1, 0, 6, 0, 545, 5504, 652036, 44013568, 11112714624, 3517475475328, 2781543486427548, 3568483481372543360, 9829161878198755474915, 48599777948701165162242560, 484370819140388708451108625276, 9036085159101926537420075859958528
Offset: 0
a(4) = 6, because there are 6 tilings of a 4 X 4 square using right trominoes and 2 X 2 tiles:
.___.___. .___.___. .___.___. .___.___. .___.___. .___.___.
| . | . | | ._|_. | | ._| . | | ._|_. | | ._|_. | | . |_. |
|___|___| |_| . |_| |_| |___| |_| ._|_| |_|_. |_| |___| |_|
| . | . | | |___| | | |___| | | |_| . | | . |_| | | |___| |
|___|___| |___|___| |___|___| |___|___| |___|___| |___|___|
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:
.___. .___. .___. .___. .___. .___. .___. .___.
| | |_|_| |___| | | | |_|_| |___| |_| | | |_|
|___| |_|_| |___| |_|_| |___| |_|_| |_|_| |_|_| .
A219975
Number of tilings of an n X n square using straight (3 X 1) trominoes and 2 X 2 tiles.
Original entry on oeis.org
1, 0, 1, 2, 3, 28, 267, 2744, 66653, 2766100, 141365332, 13305552648, 2149055591278, 493880634209398, 192321197859269019, 124351154502319720238, 122893248485909264026734, 199405053536180281080458422, 527809383857797224536981601752
Offset: 0
a(4) = 3, because there are 3 tilings of a 4 X 4 square using straight (3 X 1) trominoes and 2 X 2 tiles:
._._____. ._____._. ._._._._.
| |_____| |_____| | | . | . |
| | . | | | | . | | |___|___|
|_|___| | | |___|_| | . | . |
|_____|_| |_|_____| |___|___| .
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 1-7 of 7 results.