%I #16 Nov 28 2016 02:43:47

%S 1,1,1,1,7,15,25,37,100,229,454,811,1732,3777,7858,15339,31273,65536,

%T 136600,276535,562728,1159942,2400783,4918159,10052140,20627526,

%U 42480474,87254743,178855138,366854368

%N The number of tilings of an 8 X n floor with 1 X 4 tetrominoes.

%C Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving rectangular regions...</a>, arXiv:1311.6135 [math.CO], 2013, Table 37.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1406.7788">Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices</a>, arXiv:1406.7788 [math.CO], 2014, eq. (28).

%F G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.

%p p := (1-x)^3*(x+1)^3*(x^2+1)^3*(x^6-x^4-x^3-x^2+1) ;

%p q := -x^2 -13*x^10 -5*x^18 +8*x^6 -x -x^20 -9*x^4 +16*x^8 -13*x^12 -2*x^19 +1 +10*x^14 +5*x^7 +6*x^15 -6*x^11 +x^22 +6*x^16 +x^17 +2*x^5 -2*x^13 ;

%p taylor(p/q,x=0,30) ;

%p gfun[seriestolist](%) ;

%Y Cf. A003269 (4 X n floor), A236579 - A236581.

%Y Column k=4 of A250662.

%Y Cf. A251074.

%K nonn,easy

%O 0,5

%A _R. J. Mathar_, Jan 29 2014