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

%I A257866 #11 Feb 06 2017 14:35:49
%S A257866 1,1,3,5,19,74,209,572,1479,4304,13002,38315,109651,308982,884120,
%T A257866 2560952,7428183,21413028,61433280,176415916,507985116,1464725431,
%U A257866 4220293147,12145885239,34945690653,100586823613,289649303130,834087280681,2401368817168,6912685066843
%N A257866 Number of tilings of a 5 X n rectangle using n pentominoes of shapes W, I, L.
%H A257866 Alois P. Heinz, <a href="/A257866/b257866.txt">Table of n, a(n) for n = 0..1000</a>
%H A257866 Vaclav Kotesovec, <a href="/A257866/a257866.txt">G.f. and the recurrence (of order 315)</a>
%H A257866 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F A257866 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
%e A257866 a(3) = 5:
%e A257866 ._____. ._____. ._____. ._____. ._____.
%e A257866 | | | | | |_. | | ._| | | | ._| |_. | |
%e A257866 | | | | | | | | | | | | | | | | | | | |
%e A257866 | | | | | | | | | | | | | | | | | | | |
%e A257866 | | | | | | |_| |_| | | | |_| | | |_| |
%e A257866 |_|_|_| |_|___| |___|_| |_|___| |___|_|.
%e A257866 a(4) = 19:
%e A257866 ._______. ._______.
%e A257866 |_. |_. | | | ._| |
%e A257866 | |_. | | | | | | |
%e A257866 |_. |_| | | | | | |
%e A257866 | |___|_| | |_| | |
%e A257866 |_______| |_|___|_| ... .
%Y A257866 Cf. A174249, A233427, A234312, A234931, A247443, A247680, A249762.
%K A257866 nonn
%O A257866 0,3
%A A257866 _Alois P. Heinz_, May 11 2015