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A227959 Number of tilings using monominoes and L-trominoes in 2 X n chessboard, such that three monominoes cannot occur together in shape of L-tromino.

%I A227959 #38 Sep 08 2022 08:46:05
%S A227959 1,1,4,6,20,38,104,220,556,1244,3024,6944,16576,38536,91216,213280,
%T A227959 502864,1178928,2774592,6512864,15315072,35969952,84550912,198634048,
%U A227959 466825152,1096838208,2577550336,6056474880,14232064256,33441977216,78583660288,184655188480
%N A227959 Number of tilings using monominoes and L-trominoes in 2 X n chessboard, such that three monominoes cannot occur together in shape of L-tromino.
%H A227959 Gopinath A. R., <a href="/A227959/b227959.txt">Table of n, a(n) for n = 0..200</a>
%H A227959 Calvin Lin, <a href="https://brilliant.org/i/AQs2Zw/">Tiling</a>, Discrete Mathematics Problem on Linear Recurrence Relations, Brilliant.
%H A227959 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,2,2,4).
%F A227959 a(n) = 4*a(n-2) + 2*a(n-3) + 2*a(n-4) + 4*a(n-5), with a(0)=1, a(1)=1, a(2)=4, a(3)=6, and a(4)=20.
%F A227959 G.f.: (1+x)/(1-4*x^2-2*x^3-2*x^4-4*x^5).
%F A227959 Asymptotic formula: a(n) ~ 0.581189405182598 * 2.3498153157195^n.
%t A227959 LinearRecurrence[{0, 4, 2, 2, 4}, {1, 1, 4, 6, 20}, 33] (* or *) CoefficientList[Series[(1 + x)/(1 - 4 x^2 - 2 x^3 - 2 x^4 - 4 x^5), {x, 0, 33}], x] (* _Vincenzo Librandi_, Apr 30 2018 *)
%o A227959 (Sage)
%o A227959 fx = (1+x)/(1-4*x^2-2*x^3-2*x^4-4*x^5)
%o A227959 fxt = taylor(fx,x,0,50)
%o A227959 for i in range(51):
%o A227959     print(i, fxt.coefficient(x,i))
%o A227959 (PARI) Vec( (1+x)/(1-4*x^2-2*x^3-2*x^4-4*x^5) +O(x^66) ) \\ _Joerg Arndt_, Aug 07 2013
%o A227959 (Magma) I:=[1,1,4,6,20]; [n le 5 select I[n] else 4*Self(n-2)+2*Self(n-3)+ 2*Self(n-4)+4*Self(n-5): n in [1..35]]; // _Vincenzo Librandi_, Apr 30 2018
%Y A227959 Cf. A127864.
%K A227959 nonn,easy
%O A227959 0,3
%A A227959 _Gopinath A. R._, Aug 01 2013