cp's OEIS Frontend

A233266 Number of tilings of a 4 X n rectangle using tetrominoes of shapes L, T, Z.

%I A233266 #18 Jan 27 2025 10:31:50
%S A233266 1,0,2,10,24,70,276,820,2616,8702,27902,89500,291050,939222,3029950,
%T A233266 9798606,31657182,102237766,330356240,1067310022,3447911968,
%U A233266 11139391996,35988377472,116265759012,375619824338,1213515477460,3920484872552,12665878390278
%N A233266 Number of tilings of a 4 X n rectangle using tetrominoes of shapes L, T, Z.
%H A233266 Alois P. Heinz, <a href="/A233266/b233266.txt">Table of n, a(n) for n = 0..1000</a>
%H A233266 Nicolas Bělohoubek and Antonín Slavík, <a href="https://msekce.karlin.mff.cuni.cz/~slavik/papers/L-tetromino-tilings.pdf">L-Tetromino Tilings and Two-Color Integer Compositions</a>, Univ. Karlova (Czechia, 2025). See p. 10.
%H A233266 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%H A233266 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, 4, -6, -28, 15, 4, -13, 20, -4, 16, -10, 8, -2).
%F A233266 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).
%e A233266 a(3) = 10:
%e A233266 ._____.  ._____.  ._____.  ._____.  ._____.
%e A233266 | |_. |  | ._| |  | .___|  |___. |  | .___|
%e A233266 |_. | |  | | ._|  |_| | |  | | |_|  |_| ._|
%e A233266 | |_|_|  |_|_| |  | ._| |  | |_. |  |___| |
%e A233266 |_____|  |_____|  |_|___|  |___|_|  |_____|
%e A233266 ._____.  ._____.  ._____.  ._____.  ._____.
%e A233266 | ._| |  | |_. |  |_. ._|  |_. ._|  |___. |
%e A233266 | |_. |  | ._| |  | |_| |  | |_| |  |_. |_|
%e A233266 |_| |_|  |_| |_|  | |_. |  | ._| |  | |___|
%e A233266 |_____|  |_____|  |___|_|  |_|___|  |_____|.
%Y A233266 Cf. A084480, A174248, A226322, A230031, A232497, A233139, A233191, A242636.
%K A233266 nonn,easy
%O A233266 0,3
%A A233266 _Alois P. Heinz_, Dec 06 2013