%I #17 Nov 05 2025 15:22:26

%S 1,4,25,154,943,5773,35344,216388,1324801,8110882,49657576,304020556,

%T 1861317163,11395616227,69767835259,427142397547,2615110919020,

%U 16010597772667,98022320649478,600125959188877,3674175070596919,22494548423870416,137719270059617428

%N The number of tilings of a 6 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="https://arxiv.org/abs/1311.6135">Paving rectangular regions...</a>, arXiv:1311.6135, Table 35.

%H R. J. Mathar, <a href="https://arxiv.org/abs/1406.7788">Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices</a>, arXiv:1406.7788 [math.CO], eq. (26).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6,4,-1).

%F G.f.: (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4).

%p g := (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4) ;

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

%p gfun[seriestolist](%) ;

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

%K easy,nonn

%O 0,2

%A _R. J. Mathar_, Jan 29 2014