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

4,2

Links

Table of n, a(n) for n=4..30.

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).

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)).

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 *)

Crossrefs

Cf. A081038, A269914, A269916, A269917.

Sequence in context: A186244 A255447 A029870 * A273393 A231430 A269916

Adjacent sequences: A269912 A269913 A269914 * A269916 A269917 A269918

Keyword

nonn

Author

Marko Riedel, Mar 07 2016

Status

approved