a(1)=44.
t1,t2,t3 is a tromino standing on 1,2,3 cubes respectively.
1) Two t2-tiles generate a C-profile or a D-profile in 4 ways each.
C,D-profile: 4,2 rotation images, D-profile: 2 ways for each image.
C-profile D-profiles
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2) t1+t3 generates a C-profile in 4*2=8 ways.
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1,2) There are 12 ways to generate a C-profile. The connection of two C-profiles is a 2 X 2 X 3 cuboid. Starting with a C-profile, there are 4*3*3=36 ways to generate this cuboid.
3) There are 4*2=8 ways to generate the cuboid by starting with a D-profile. Therefore, a(1)=36+8=44.
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