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Number of tilings of a 4 X n rectangle using integer-sided rectangular tiles of equal area.
2

%I #12 Sep 05 2021 19:15:17

%S 1,3,9,20,49,115,343,850,2401,6698,18677,52383,148417,418280,1184717,

%T 3357537,9518235,27001128,76637532,217530615,617624137,1753811531,

%U 4980521844,14144892243,40174244540,114105904403,324101321331,920579535645,2614852152957

%N Number of tilings of a 4 X n rectangle using integer-sided rectangular tiles of equal area.

%C a(n+1)/a(n) tends to r = (1+sqrt(29)+sqrt(2*(7+sqrt(29))))/4 = 2.840536194094952533051131..., where r is the largest root of x^4-x^3-5*x^2-x+1. - _Vaclav Kotesovec_, Dec 21 2012

%H Alois P. Heinz, <a href="/A220770/b220770.txt">Table of n, a(n) for n = 0..1000</a>

%e a(2) = 9:

%e .___. .___. .___. .___. .___. .___. .___. .___. .___.

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

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

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

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

%Y Column k=4 of A220777.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 19 2012