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%I #34 Sep 16 2020 07:44:42
%S 0,0,1,5,18,58,177,522,1503,4252,11869,32787,89821,244415,661415,
%T 1781654,4780776,12786704,34104792,90749209,240982564,638800052,
%U 1690764378,4469170031,11799684559,31122693066,82016622160,215969175981,568313267862,1494601936229
%N Number of words of length n over the alphabet {0,1,2} that contain the substring 12 but not the substring 01.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-5,1).
%F a(n) = Sum_{i=1..n} A001906(n-i) * A052921(i-1).
%F G.f.: x^2*(x-1)/((x^2-3*x+1)*(x^3-2*x^2+3*x-1)). - _Alois P. Heinz_, Sep 15 2020
%e a(0) = a(1) = 0, because no word of length n < 2 can contain 12.
%e a(2) = 1, because there is one word of length 2 and it is 12.
%e a(3) = 5, because there are 5 words of length 3 and they are 121, 112, 212, 122, 120.
%Y Cf. A001906, A052921.
%K nonn,easy
%O 0,4
%A _Mauricio J. Santos_, Sep 15 2020
%E a(20)-a(29) from _Alois P. Heinz_, Sep 15 2020
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