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A233139 Number of tilings of a 4 X n rectangle using T and Z tetrominoes. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A100132

Adjacent sequences:  A233136 A233137 A233138 * A233140 A233141 A233142

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 04 2013

STATUS

approved

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Last modified October 20 17:28 EDT 2019. Contains 328268 sequences. (Running on oeis4.)