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%I #28 Oct 30 2022 18:19:59
%S 1,1,13,43,269,1213,6427,31387,159651,795611,4005785,20064827,
%T 100764343,505375405,2536323145,12724855013,63851706457,320373303983,
%U 1607526474153,8065864257905,40471399479495,203068825478591,1018918472214687,5112520236292975,25652573037707685
%N Number of ways to tile a 6 X n rectangle with 1 X 1 and 2 X 2 tiles.
%H Vincenzo Librandi, <a href="/A063650/b063650.txt">Table of n, a(n) for n = 0..1000</a>
%H R. J. Mathar, <a href="http://arxiv.org/abs/1609.03964">Tiling nXm rectangles with 1X1 and sXs squares</a> arXiv:1609.03964 [math.CO] (2016) Section 4.1.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,16,1,-27,1,4).
%F G.f.: ( -1+x+5*x^2-x^4 ) / ( -1+2*x+16*x^2+x^3-27*x^4+x^5+4*x^6 ).
%F a(n) = 2a(n-1) + 16a(n-2) + a(n-3) - 27a(n-4) + a(n-5) + 4a(n-6) - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006
%t LinearRecurrence[{2, 16, 1, -27, 1, 4}, {1, 1, 13, 43, 269, 1213}, 22] (* _Jean-François Alcover_, Oct 30 2018 *)
%t CoefficientList[Series[(-1+x+5*x^2-x^4)/(-1+2*x+16*x^2+x^3-27*x^4+x^5+4*x^6), {x, 0, 50}], x] (* _Stefano Spezia_, Oct 30 2018 *)
%o (Magma) I:=[1,1,13,43,269,1213]; [n le 6 select I[n] else 2*Self(n-1)+16*Self(n-2)+Self(n-3)-27*Self(n-4)+Self(n-5)+4*Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Oct 30 2018
%Y Cf. A001045, A054854, A054855, A063650-A063654.
%Y Column k=6 of A245013.
%K nonn
%O 0,3
%A _Reiner Martin_, Jul 23 2001
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