%I #19 Jun 10 2022 06:14:13

%S 1,5,37,269,1949,14121,102313,741305,5371097,38916077,281964941,

%T 2042966149,14802232757,107249008849,777068573905,5630220503025,

%U 40793546383409,295568073335893,2141527121824885,15516352499614333,112423136012925517,814557513519681785

%N The number of tilings of a 7 X (4n) 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 Mudit Aggarwal and Samrith Ram, <a href="https://arxiv.org/abs/2206.04437">Generating functions for straight polyomino tilings of narrow rectangles</a>, arXiv:2206.04437 [math.CO], 2022.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings</a>, arXiv:1311.6135 [math.CO], 2013, Table 36.

%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], eq. (27).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-6,4,-1).

%F G.f.: (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4).

%p g := (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4) ;

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

%p gfun[seriestolist](%) ;

%t LinearRecurrence[{8, -6, 4, -1}, {1, 5, 37, 269}, 19] (* _Jean-François Alcover_, Feb 19 2019 *)

%Y Cf. A003269 (4Xn floor), A236579 - A236582.

%K nonn

%O 0,2

%A _R. J. Mathar_, Jan 29 2014