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A247125
Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, X.
7
1, 0, 2, 1, 16, 10, 59, 60, 330, 397, 1520, 2218, 7875, 12820, 39250, 70045, 202168, 384866, 1038051, 2073580, 5385754, 11156701, 28015232, 59580154, 146333795, 317517636, 766142242, 1686735709, 4019319048, 8946988370, 21116854115, 47386013020, 111065223914
OFFSET
0,3
FORMULA
G.f.: -1/(2*x^6+6*x^5+12*x^4+x^3+2*x^2-1).
EXAMPLE
a(4) = 16:
._______. ._______. ._______.
| ._____| | ._____| | ._| ._|
|_| |_. | |_| |_. | | | | | |
|_. ._| | |_. ._| | | | | | |
| |_|___| | |_| | | |_| |_| |
|_______| (2) |_____|_| (4) |___|___| (4)
._______. ._______.
| ._____| | ._____|
|_| ._. | |_|_. | |
| |_| |_| | ._| | |
|_____| | | |___| |
|_______| (2) |___|___| (4) .
MAPLE
a:= n-> (<<0|1|0|0|0|0>, <0|0|1|0|0|0>, <0|0|0|1|0|0>,
<0|0|0|0|1|0>, <0|0|0|0|0|1>, <2|6|12|1|2|0>>^n)[6, 6]:
seq(a(n), n=0..40);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 19 2014
STATUS
approved