A233191 Number of tilings of a 4 X n rectangle using L and T tetrominoes.

1, 0, 2, 4, 12, 16, 76, 128, 386, 832, 2368, 5024, 13946, 31680, 82632, 193696, 498174, 1182464, 2993384, 7213648, 18061074, 43832960, 109163384, 266217472, 660116398, 1615451648, 3995295112, 9796774896, 24189684402, 59396496000, 146494223160, 360026507808

Offset: 0

Author

Alois P. Heinz, Dec 05 2013

Keywords

• nonn
• easy

Examples

			a(3) = 4:
._____.  ._____.  ._____.  ._____.
|_. ._|  |_. ._|  | |_. |  | ._| |
| |_| |  | |_| |  | ._| |  | |_. |
| ._| |  | |_. |  |_| |_|  |_| |_|
|_|___|  |___|_|  |_____|  |_____|.
		

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 (0, 4, 4, 5, -8, 4, 12, -18, -8, 0, 0, -8).

Crossrefs

Cf. A084480, A174248, A226322, A230031, A232497, A233139, A233266.

Programs

Maple

gf:= (2*x^6+x^4+2*x^2-1) / (-8*x^12 -8*x^9 -18*x^8
     +12*x^7 +4*x^6 -8*x^5 +5*x^4 +4*x^3 +4*x^2 -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Formula

G.f.: (2*x^6+x^4+2*x^2-1) / (-8*x^12 -8*x^9 -18*x^8 +12*x^7 +4*x^6 -8*x^5 +5*x^4 +4*x^3 +4*x^2 -1).