A269915 Number of ternary strings of length n with maximal run length three containing 1112.

1, 5, 21, 80, 287, 993, 3347, 11067, 36055, 116089, 370222, 1171353, 3681375, 11504101, 35772799, 110760185, 341640131, 1050254568, 3218970519, 9839399805, 30002862947, 91284474775, 277176264351, 840067321393, 2541769382014, 7678558044741, 23163047559031

Offset: 4

Author

Marko Riedel, Mar 07 2016

Keywords

• nonn

Links

• Math StackExchange, Words built with 0,1,2
• Marko Riedel, Maple code by total enumeration and by generating function.
• Index entries for linear recurrences with constant coefficients, signature (3,3,-1,-13,-23,-25,-18,-8,-2).

Crossrefs

Cf. A081038, A269914, A269916, A269917.

Programs

Mathematica

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 *)

Formula

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)).