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A257866 Number of tilings of a 5 X n rectangle using n pentominoes of shapes W, I, L. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 24 17:36 EST 2020. Contains 338616 sequences. (Running on oeis4.)