A232497 Number of tilings of a 4 X n rectangle using L and Z tetrominoes.

1, 0, 2, 6, 14, 32, 102, 238, 652, 1696, 4480, 11658, 30870, 80644, 212292, 556858, 1463390, 3840686, 10090218, 26490280, 69575414, 182693434, 479789138, 1259906496, 3308668718, 8688615148, 22817011182, 59918425698, 157349755400, 413208421354, 1085110433096

Offset: 0

Author

Alois P. Heinz, Nov 24 2013

Keywords

• nonn
• easy

Examples

			a(3) = 6:
._._._.  ._._._.  ._._._.  ._._._.  ._._._.  ._._._.
| .___|  |___. |  | |_. |  | ._| |  | .___|  |___. |
|_| ._|  |_. |_|  |_. | |  | | ._|  |_| | |  | | |_|
|___| |  | |___|  | |_|_|  |_|_| |  | ._| |  | |_. |
|_____|  |_____|  |_____|  |_____|  |_|___|  |___|_|.
		

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 (0,5,7,2,-13,-13,-6,-6,0,-4,0,-2).

Crossrefs

Cf. A084480, A174248, A226322, A233139, A233191, A233266.

Programs

Maple

a:= n-> coeff(series(-(x^6-x^5-2*x^4+x^3+3*x^2-1)/
    (2*x^12+4*x^10+6*x^8+6*x^7+13*x^6+13*x^5-2*x^4-7*x^3-5*x^2+1),
    x, n+1), x, n);
seq(a(n), n=0..40);

Formula

G.f.: -(x^6-x^5-2*x^4+x^3+3*x^2-1) / (2*x^12 +4*x^10 +6*x^8 +6*x^7 +13*x^6 +13*x^5 -2*x^4 -7*x^3 -5*x^2+1).