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Number of tilings of a 3 X n rectangle using integer-sided rectangular tiles of equal area.
2

%I #12 Sep 05 2021 19:15:39

%S 1,2,6,4,20,7,54,12,190,23,616,44,2266,91,8136,198,30214,409,111540,

%T 875,415601,1887,1546170,4026,5767198,8649,21503856,18583,80237366,

%U 39868,299369546,85629,1117185300,183962,4169054092,395051,15558753295,848494,58064626980

%N Number of tilings of a 3 X n rectangle using integer-sided rectangular tiles of equal area.

%C a(n)^(1/n) tends to sqrt(2+sqrt(3)) = 1.93185165257813657349... if n is even and to r = (1 + ((29 - 3*sqrt(93))/2)^(1/3) + ((29 + 3*sqrt(93))/2)^(1/3))/3 = 1.46557123187676802665... (where r is the real root of the equation r^2*(r-1) = 1) if n is odd. - _Vaclav Kotesovec_, Sep 07 2016

%H Alois P. Heinz, <a href="/A220769/b220769.txt">Table of n, a(n) for n = 0..1000</a>

%e a(5) = 7:

%e ._________. ._________. ._________. ._________.

%e | | |_________| | | | | | | |_____| | |

%e | | |_________| | | | | | | |_____| | |

%e |_________| |_________| |_|_|_|_|_| |_____|_|_|

%e ._________. ._________. ._________.

%e | |_____| | | | |_____| |_|_|_|_|_|

%e | |_____| | | | |_____| |_|_|_|_|_|

%e |_|_____|_| |_|_|_____| |_|_|_|_|_|

%Y Column k=3 of A220777.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 19 2012