A257866 Number of tilings of a 5 X n rectangle using n pentominoes of shapes W, I, L.

1, 1, 3, 5, 19, 74, 209, 572, 1479, 4304, 13002, 38315, 109651, 308982, 884120, 2560952, 7428183, 21413028, 61433280, 176415916, 507985116, 1464725431, 4220293147, 12145885239, 34945690653, 100586823613, 289649303130, 834087280681, 2401368817168, 6912685066843

Offset

0,3

Links

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

Vaclav Kotesovec, G.f. and the recurrence (of order 315)

Wikipedia, Pentomino

Formula

a(n) ~ c * d^n, where d = 2.878962978866730659679600165158895088546680936475540731494833253735549346144..., c = 0.33249894796240209167801000207088312509480543003269025485052861968247997... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

Example

a(3) = 5:
._____. ._____. ._____. ._____. ._____.
| | | | | |_. | | ._| | | | ._| |_. | |
| | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
| | | | | | |_| |_| | | | |_| | | |_| |
|_|_|_| |_|___| |___|_| |_|___| |___|_|.
a(4) = 19:
._______. ._______.
|_. |_. | | | ._| |
| |_. | | | | | | |
|_. |_| | | | | | |
| |___|_| | |_| | |
|_______| |_|___|_| ... .

Crossrefs

Cf. A174249, A233427, A234312, A234931, A247443, A247680, A249762.

Sequence in context: A182357 A181519 A265778 * A251617 A055452 A184254

Adjacent sequences: A257863 A257864 A257865 * A257867 A257868 A257869

Keyword

nonn

Author

Alois P. Heinz, May 11 2015

Status

approved