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%I #38 Jun 27 2020 03:49:53
%S 1,1,3,10,23,62,170,441,1173,3127,8266,21937,58234,154390,409573,
%T 1086567,2882021,7645046,20279829,53794224,142696606,378522507,
%U 1004078871,2663452699,7065162260,18741269167,49713692146,131872134232,349808216915,927912454723
%N Number of tilings of a 3 X n rectangle with n trominoes.
%D G. Kreweras, Recouvrements d'un rectangle de largeur 3 à l'aide de triminos, Mathématiques et sciences humaines, tome 130 (1995), p. 27-31.
%H Alois P. Heinz, <a href="/A134438/b134438.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tromino">Tromino</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,6,1,0,-1).
%F a(n) = a(n-1) +2*a(n-2) +6*a(n-3) +a(n-4) -a(n-6).
%F G.f.: (1-x^3) / (1-x-2*x^2-6*x^3-x^4+x^6). - _Alois P. Heinz_, Oct 09 2008
%p a:= n-> (Matrix([[1$2, 0$2, 1, 0]]). Matrix(6, (i,j)-> if i+1=j then 1 elif j=1 then [1, 2, 6, 1, 0, -1][i] else 0 fi)^n)[1,2]: seq(a(n), n=0..30); # _Alois P. Heinz_, Oct 09 2008
%t LinearRecurrence[{1,2,6,1,0,-1},{1,1,3,10,23,62},40] (* _Harvey P. Dale_, Aug 27 2013 *)
%Y Cf. A174248, A174249, A174250, A174251, A174252, A174253, A215826, A233290, A269664, A270063.
%Y Column k=3 of A233320.
%K nonn,easy
%O 0,3
%A _Philippe Deléham_, Jan 18 2008
%E More terms from _Alois P. Heinz_, Oct 09 2008
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