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

%I #17 Sep 05 2021 19:16:01

%S 1,2,4,6,9,11,21,24,43,62,102,147,259,380,636,1003,1640,2587,4258,

%T 6768,11053,17740,28806,46371,75318,121405,196800,317874,514870,

%U 832043,1347376,2178312,3526218,5703039,9230054,14930386,24162313,39088172,63252756,102334540

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

%C a(n+1)/a(n) tends to phi = (1+sqrt(5))/2 = A001622. - _Vaclav Kotesovec_, Dec 21 2012

%H Alois P. Heinz, <a href="/A220768/b220768.txt">Table of n, a(n) for n = 0..1000</a>

%e a(5) = 11:

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

%e | | |_________| | | | | | | |___| | | | | |___| | |

%e |_________| |_________| |_|_|_|_|_| |___|_|_|_| |_|___|_|_|

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

%e | | |___| | | | | |___| |___|___| | |___| |___| | |___|___|

%e |_|_|___|_| |_|_|_|___| |___|___|_| |___|_|___| |_|___|___|

%e ._________.

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

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

%Y Column k=2 of A220777.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 19 2012