A269916 Number of ternary strings of length n with maximal run length four containing 11112.

1, 5, 21, 81, 296, 1043, 3585, 12095, 40221, 132225, 430633, 1391623, 4467689, 14262766, 45311977, 143343279, 451768405, 1419092951, 4444424613, 13882255419, 43256925753, 134492621659, 417322590000, 1292554593007, 3996626787973, 12338508959035, 38037021764053

Offset

5,2

Links

Table of n, a(n) for n=5..31.

Math StackExchange, Words built with 0,1,2

Marko Riedel, Maple code by total enumeration and by generating function.

Formula

G.f.: x^5*(x+1)*(x^2+1)*(x^4+x^3+x^2+x+1) / ((x^8+3*x^7+5*x^6+7*x^5 +7*x^4+5*x^3+3*x^2+x-1) * (2*x^4+2*x^3+2*x^2+2*x-1)).

Mathematica

Drop[CoefficientList[Series[x^5 (x + 1) (x^2 + 1) (x^4 + x^3 + x^2 + x + 1)/((x^8 + 3 x^7 + 5 x^6 + 7 x^5 + 7 x^4 + 5 x^3 + 3 x^2 + x - 1) (2 x^4 + 2 x^3 + 2 x^2 + 2 x - 1)), {x, 0, 31}], x], 5] (* Michael De Vlieger, Mar 08 2016 *)

Crossrefs

Cf. A081038, A269914, A269915, A269917.

Sequence in context: A269915 A273393 A231430 * A273205 A269917 A081038

Adjacent sequences: A269913 A269914 A269915 * A269917 A269918 A269919

Keyword

nonn

Author

Marko Riedel, Mar 07 2016

Status

approved