A247125 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, X.

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

Author

Alois P. Heinz, Nov 19 2014

Keywords

• nonn

Examples

			a(4) = 16:
._______.     ._______.     ._______.
| ._____|     | ._____|     | ._| ._|
|_| |_. |     |_| |_. |     | | | | |
|_. ._| |     |_. ._| |     | | | | |
| |_|___|     | |_| | |     |_| |_| |
|_______| (2) |_____|_| (4) |___|___| (4)
._______.     ._______.
| ._____|     | ._____|
|_| ._. |     |_|_. | |
| |_| |_|     | ._| | |
|_____| |     | |___| |
|_______| (2) |___|___| (4) .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Pentomino
• Index entries for linear recurrences with constant coefficients, signature (0,2,1,12,6,2).

Crossrefs

Cf. A174249, A233427, A234312, A247124, A247268.

Programs

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);

Formula

G.f.: -1/(2*x^6+6*x^5+12*x^4+x^3+2*x^2-1).