A233139 Number of tilings of a 4 X n rectangle using T and Z tetrominoes.
1, 0, 0, 0, 2, 4, 8, 18, 44, 104, 242, 564, 1320, 3090, 7228, 16904, 39538, 92484, 216328, 506002, 1183564, 2768424, 6475506, 15146580, 35428712, 82869778, 193837148, 453396168, 1060519538, 2480615780, 5802302024, 13571915922, 31745486700, 74254506984
Offset: 0
Examples
a(5) = 4: ._____.___. .___._____. ._._____._. ._._____._. |_. ._| ._| |_. |_. ._| | |_. ._| | | |_. ._| | | |_|___| | | |___|_| | | ._|_|_. | | ._|_|_. | | ._| |_. | | ._| |_. | |_| |_. |_| |_| ._| |_| |_|_____|_| |_|_____|_| |_____|___| |___|_____|.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Wikipedia, Tetromino
- Index entries for linear recurrences with constant coefficients, signature (2,0,1,2).
Programs
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Maple
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|1|0|2>>^n. <<1, 0, 0, 0>>)[1, 1]: seq(a(n), n=0..40);
Formula
G.f.: (x^3+2*x-1) / (2*x^4+x^3+2*x-1).
a(n) = 2*a(n-1)+a(n-3)+2*a(n-4) for n>3, a(0)=1, a(1)=a(2)=a(3)=0.