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A247680 Number of tilings of a 5 X n rectangle using n pentominoes of shapes W, I, L, F. 8
1, 1, 3, 5, 21, 82, 249, 688, 1879, 5690, 17932, 55271, 164427, 485348, 1451110, 4395114, 13313135, 40073992, 120200822, 360897368, 1086543152, 3274191643, 9858847241, 29657925485, 89206237151, 268435863317, 808022052324, 2432169981689, 7319562671432 (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 324)

Wikipedia, Pentomino

FORMULA

a(n) ~ c * d^n, where d = 3.009533036298033336764263169394953980849599088993157702490314631810945318907..., c = 0.29272000293879867768013500033525343337565088925220444775140709413075274... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

EXAMPLE

a(3) = 5:

._____.  ._____.  ._____.  ._____.  ._____.

| | | |  | |_. |  | ._| |  | | ._|  |_. | |

| | | |  | | | |  | | | |  | | | |  | | | |

| | | |  | | | |  | | | |  | | | |  | | | |

| | | |  | | |_|  |_| | |  | |_| |  | |_| |

|_|_|_|  |_|___|  |___|_|  |_|___|  |___|_|.

a(4) = 21:

._______.  ._______.

|_. |_. |  | ._| ._|

| |_. | |  | |_. | |

|_. |_| |  | | |_| |

| |___|_|  |_| ._| |

|_______|  |___|___| ... .

CROSSREFS

Cf. A174249, A233427, A234312, A234931, A247443, A249762, A257866.

Sequence in context: A196418 A189560 A216385 * A179265 A084253 A153889

Adjacent sequences:  A247677 A247678 A247679 * A247681 A247682 A247683

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2014

STATUS

approved

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)