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A242636 Number of tilings of a 4 X n rectangle using tetrominoes of shapes L, Z, O. 2
1, 0, 3, 12, 23, 94, 289, 842, 2771, 8510, 26411, 83122, 258199, 805914, 2517287, 7846960, 24490017, 76416244, 238387767, 743840496, 2320800841, 7240890040, 22592311143, 70488834118, 219928631821, 686190651342, 2140948175385, 6679872756528, 20841562274863 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Tetromino

FORMULA

G.f.: (x^6-x^5-2*x^4+x^3+3*x^2-1) / (-2*x^12 -4*x^10 -2*x^9 +x^8 -3*x^7 -13*x^6 -18*x^5 +3*x^4 +13*x^3 +6*x^2 -1).

EXAMPLE

a(3) = 12:

._____.  ._____.  .___._.  ._.___.  ._____.  ._____.

| .___|  |___. |  |   | |  | |   |  |___. |  | .___|

|_|_. |  | ._|_|  |___| |  | |___|  |   |_|  |_|   |

|   | |  | |   |  | |___|  |___| |  |___| |  | |___|

|___|_|  |_|___|  |_____|  |_____|  |_____|  |_____|

._____.  ._____.  ._.___.  .___._.  ._____.  ._____.

| .___|  |___. |  | |_. |  | ._| |  | .___|  |___. |

|_| ._|  |_. |_|  |_. | |  | | ._|  |_| | |  | | |_|

|___| |  | |___|  | |_|_|  |_|_| |  | ._| |  | |_. |

|_____|  |_____|  |_____|  |_____|  |_|___|  |___|_|.

MAPLE

gf:= (x^6-x^5-2*x^4+x^3+3*x^2-1) / (-2*x^12 -4*x^10 -2*x^9 +x^8 -3*x^7 -13*x^6 -18*x^5 +3*x^4 +13*x^3 +6*x^2 -1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..40);

CROSSREFS

Cf. A084480, A174248, A226322, A230031, A232497, A233139, A233191, A233266.

Sequence in context: A063107 A015629 A154138 * A012469 A103449 A030571

Adjacent sequences:  A242633 A242634 A242635 * A242637 A242638 A242639

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, May 19 2014

STATUS

approved

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Last modified September 23 13:55 EDT 2017. Contains 292358 sequences.