|
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 |_|_|
| 