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A234312
Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, X.
10
1, 0, 2, 0, 4, 2, 8, 8, 16, 24, 36, 64, 88, 160, 224, 392, 576, 960, 1472, 2368, 3728, 5888, 9376, 14720, 23488, 36896, 58752, 92544, 146944, 232064, 367680, 581632, 920448, 1457152, 2305024, 3649664, 5773312, 9140224, 14460928, 22890496, 36221184, 57327616
OFFSET
0,3
FORMULA
G.f.: -1/(2*x^5+2*x^2-1).
a(n) = 2*(a(n-2)+a(n-5)) for n>4, a(1)=a(3)=0, a(0)=1, a(2)=2, a(4)=4.
EXAMPLE
a(4) = 4:
._______. ._______. ._______. ._______.
|_. |_. | | ._| ._| |_. | ._| | ._|_. |
| | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
| |_| |_| |_| |_| | | |_|_| | |_| | |_|
|___|___| |___|___| |___|___| |___|___|.
a(5) = 2:
._________. ._________.
| | ._____| |_____. | |
| |_| |_. | | ._| |_| |
| |_. ._| | | |_. ._| |
|___|_| | | | | |_|___|
|_______|_| |_|_______|.
MAPLE
a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
<0|0|0|0|1>, <2|0|0|2|0>>^n)[5, 5]:
seq(a(n), n=0..50);
MATHEMATICA
LinearRecurrence[{0, 2, 0, 0, 2}, {1, 0, 2, 0, 4}, 50] (* Jean-François Alcover, May 28 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 23 2013
STATUS
approved