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%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