|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|