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A236577 The number of tilings of a 6 X n floor with 1 X 3 trominoes.

%I A236577 #20 Nov 15 2021 12:20:23
%S A236577 1,1,1,6,13,22,64,155,321,783,1888,4233,9912,23494,54177,126019,
%T A236577 295681,687690,1600185,3738332,8712992,20293761,47337405,110368563,
%U A236577 257206012,599684007,1398149988,3259051800,7597720649,17712981963
%N A236577 The number of tilings of a 6 X n floor with 1 X 3 trominoes.
%C A236577 Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.
%H A236577 G. C. Greubel, <a href="/A236577/b236577.txt">Table of n, a(n) for n = 0..1000</a>
%H A236577 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 21.
%H A236577 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 (14).
%H A236577 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,7,-1,-5,-10,-1,3,5,1,-1,-1).
%F A236577 G.f.: See the definition of g in the Maple code.
%p A236577 g := (1-x^3)^2*(-x^2+1-x^3)/ (-x^10+x^12+x^11+10*x^6-5*x^9-3*x^8+x^7+x^4-7*x^3+5*x^5-x^2-x+1) ;
%p A236577 taylor(%,x=0,30) ;
%p A236577 gfun[seriestolist](%) ;
%t A236577 CoefficientList[Series[(1 - x^3)^2*(-x^2 + 1 - x^3)/(-x^10 + x^12 + x^11 + 10*x^6 - 5*x^9 - 3*x^8 + x^7 + x^4 - 7*x^3 + 5*x^5 - x^2 - x + 1), {x, 0, 50}], x] (* _G. C. Greubel_, Apr 27 2017 *)
%o A236577 (PARI) x='x+O('x^50); Vec((1-x^3)^2*(-x^2+1-x^3)/(-x^10+x^12+x^11+10*x^6 -5*x^9-3*x^8+x^7+x^4-7*x^3+5*x^5-x^2-x+1)) \\ _G. C. Greubel_, Apr 27 2017
%Y A236577 Cf. A000930 (3Xn floor), A049086 (4X3n floor), A236576 - A236578.
%Y A236577 Column k=3 of A250662.
%Y A236577 Cf. A251073.
%K A236577 nonn,easy
%O A236577 0,4
%A A236577 _R. J. Mathar_, Jan 29 2014