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Number of ternary strings of length n with maximal run length three containing 1112.
6

%I #21 Sep 22 2024 09:50:43

%S 1,5,21,80,287,993,3347,11067,36055,116089,370222,1171353,3681375,

%T 11504101,35772799,110760185,341640131,1050254568,3218970519,

%U 9839399805,30002862947,91284474775,277176264351,840067321393,2541769382014,7678558044741,23163047559031

%N Number of ternary strings of length n with maximal run length three containing 1112.

%H Math StackExchange, <a href="http://math.stackexchange.com/questions/1685843">Words built with 0,1,2</a>

%H Marko Riedel, <a href="/A269915/a269915.maple.txt">Maple code by total enumeration and by generating function.</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, -1, -13, -23, -25, -18, -8, -2).

%F G.f.: x^4*(x+1)*(x^2+1)*(x^2+x+1)/ ((x^6+3*x^5+5*x^4+5*x^3+3*x^2+x-1) * (2*x^3+2*x^2+2*x-1)).

%t Drop[CoefficientList[Series[x^4 (x + 1) (x^2 + 1) (x^2 + x + 1)/((x^6 + 3 x^5 + 5 x^4 + 5 x^3 + 3 x^2 + x - 1) (2 x^3 + 2 x^2 + 2 x - 1)), {x, 0, 30}], x], 4] (* _Michael De Vlieger_, Mar 08 2016 *)

%Y Cf. A081038, A269914, A269916, A269917.

%K nonn

%O 4,2

%A _Marko Riedel_, Mar 07 2016