%I #7 Mar 14 2016 18:21:01
%S 1,2,14,93,590,3710,23509,148796,940916,5952243,37655502,238204978,
%T 1506870209,9532433288,60301864000,381467462217,2413150656124,
%U 15265511608858,96569119066667,610893045560410,3864489168524208,24446630393071735,154648573589573678
%N Number of tilings of a 3 X n rectangle using monominoes and trominoes of any shape.
%H Alois P. Heinz, <a href="/A270063/b270063.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(x^15 +2*x^14 +5*x^13 -4*x^12 -7*x^11 -21*x^10 +12*x^9 +11*x^8 +24*x^7 -21*x^6 -13*x^5 +16*x^3 +2*x^2 +2*x -1) / (x^18 +2*x^17 +5*x^16 -9*x^15 -21*x^14 -54*x^13 +32*x^12 +46*x^11 +147*x^10 +21*x^9 -40*x^8 -110*x^7 -17*x^6 -11*x^5 -32*x^4 -37*x^3 -8*x^2 -4*x +1).
%Y Column k=3 of A270061.
%Y Cf. A134438.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Mar 09 2016