%I #15 Sep 06 2021 01:45:23
%S 1,1,5,3,9,1,7,1,9,3,5,1,11,1,5,3,9,1,7,1,9,3,5,1,11,1,5,3,9,1,7,1,9,
%T 3,5,1,11,1,5,3,9,1,7,1,9,3,5,1,11,1,5,3,9,1,7,1,9,3,5,1,11,1,5,3,9,1,
%U 7,1,9,3,5,1,11,1,5,3,9,1,7,1,9,3,5,1,11
%N 1 followed by period 12: (1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11) repeated; offset 0.
%C Also the number of tilings of an n X 4 rectangle using integer-sided rectangular tiles of area n.
%H Alois P. Heinz, <a href="/A220129/b220129.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(10*x^6+11*x^5+16*x^4+9*x^3+7*x^2+2*x+1) / (x^6+x^5+x^4-x^2-x-1).
%e a(6) = 7, because there are 7 tilings of a 6 X 4 rectangle using integer-sided rectangular tiles of area 6:
%e ._._._._. ._._._._. ._._____. .___._._.
%e | | | | | | | | | | | | | | |
%e | | | | | |_____| | | |_____| | | | |
%e | | | | | | | | | | | |___| | |
%e | | | | | |_____| | | |_____| | | | |
%e | | | | | | | | | | | | | | |
%e |_|_|_|_| |_____|_| |_|_____| |___|_|_|
%e ._.___._. ._._.___. .___.___.
%e | | | | | | | | | | |
%e | | | | | | | | | | |
%e | |___| | | | |___| |___|___|
%e | | | | | | | | | | |
%e | | | | | | | | | | |
%e |_|___|_| |_|_|___| |___|___|
%p a:= n-> `if`(n=0, 1, [11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1][irem(n, 12)+1]):
%p seq(a(n), n=0..100);
%Y Row n=4 of A220122.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Dec 06 2012