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

0,5

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).

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.

Example

a(5) = 4:
._____.___.  .___._____.  ._._____._.  ._._____._.
|_. ._| ._|  |_. |_. ._|  | |_. ._| |  | |_. ._| |
| |_|___| |  | |___|_| |  | ._|_|_. |  | ._|_|_. |
| ._| |_. |  | ._| |_. |  |_| |_. |_|  |_| ._| |_|
|_|_____|_|  |_|_____|_|  |_____|___|  |___|_____|.

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);

Crossrefs

Cf. A084480, A174248, A226322, A230031, A232497, A233191, A233266.

Sequence in context: A052327 A059221 A193617 * A308246 A114203 A339837

Adjacent sequences: A233136 A233137 A233138 * A233140 A233141 A233142

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 04 2013

Status

approved