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A019439 Number of ways of tiling a 2 X n rectangle with dominoes and trominoes.

%I A019439 #38 Apr 05 2025 08:37:04
%S A019439 1,1,2,6,17,43,108,280,727,1875,4832,12470,32191,83075,214372,553214,
%T A019439 1427673,3684333,9507936,24536616,63320419,163407771,421697922,
%U A019439 1088253936,2808400703,7247494517,18703234038,48266468208,124558777387,321442392689,829529751892,2140724511882
%N A019439 Number of ways of tiling a 2 X n rectangle with dominoes and trominoes.
%C A019439 The old entry with this sequence number was a duplicate of A007737.
%D A019439 Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.
%H A019439 Alois P. Heinz, <a href="/A019439/b019439.txt">Table of n, a(n) for n = 0..2430</a>
%H A019439 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,3,2,1,-1).
%F A019439 G.f.: -(x^3+x-1)/(x^6-x^5-2*x^4-3*x^3-2*x+1). - _Alois P. Heinz_, Sep 24 2009
%p A019439 a:= n-> (Matrix([[1, 1, 0, 0, 1, 1]]). Matrix (6, (i,j)-> if i=j-1 then 1 elif j=1 then [2, 0, 3, 2, 1, -1][i] else 0 fi)^n)[1,2]: seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 24 2009
%t A019439 LinearRecurrence[{2, 0, 3, 2, 1, -1}, {1, 1, 2, 6, 17, 43}, 40] // Rest (* _Jean-François Alcover_, Feb 18 2016 *)
%Y A019439 Column k=2 of A364457.
%K A019439 nonn,easy
%O A019439 0,3
%A A019439 _N. J. A. Sloane_, Oct 04 2008
%E A019439 More terms from _Alois P. Heinz_, Sep 24 2009
%E A019439 a(0)=1 prepended by _Alois P. Heinz_, Jul 25 2023