A233266 Number of tilings of a 4 X n rectangle using tetrominoes of shapes L, T, Z.
1, 0, 2, 10, 24, 70, 276, 820, 2616, 8702, 27902, 89500, 291050, 939222, 3029950, 9798606, 31657182, 102237766, 330356240, 1067310022, 3447911968, 11139391996, 35988377472, 116265759012, 375619824338, 1213515477460, 3920484872552, 12665878390278
Offset: 0
Examples
a(3) = 10: ._____. ._____. ._____. ._____. ._____. | |_. | | ._| | | .___| |___. | | .___| |_. | | | | ._| |_| | | | | |_| |_| ._| | |_|_| |_|_| | | ._| | | |_. | |___| | |_____| |_____| |_|___| |___|_| |_____| ._____. ._____. ._____. ._____. ._____. | ._| | | |_. | |_. ._| |_. ._| |___. | | |_. | | ._| | | |_| | | |_| | |_. |_| |_| |_| |_| |_| | |_. | | ._| | | |___| |_____| |_____| |___|_| |_|___| |_____|.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Nicolas Bělohoubek and Antonín Slavík, L-Tetromino Tilings and Two-Color Integer Compositions, Univ. Karlova (Czechia, 2025). See p. 10.
- Wikipedia, Tetromino
- Index entries for linear recurrences with constant coefficients, signature (2, 4, 4, -6, -28, 15, 4, -13, 20, -4, 16, -10, 8, -2).
Formula
G.f.: (x^8 -4*x^7 +3*x^6 -2*x^5 -2*x^4 -2*x^3 +2*x^2 +2*x -1) / (-2*x^14 +8*x^13 -10*x^12 +16*x^11 -4*x^10 +20*x^9 -13*x^8 +4*x^7 +15*x^6 -28*x^5 -6*x^4 +4*x^3 +4*x^2 +2*x -1).