A269917 Number of ternary strings of length n with maximal run length five containing 111112.

1, 5, 21, 81, 297, 1052, 3635, 12333, 41255, 136449, 447147, 1454091, 4697983, 15094393, 48264551, 153678185, 487510286, 1541427097, 4859385039, 15278735029, 47923821239, 149992151725, 468512665975, 1460770946689, 4546890238683, 14131055304241, 43854326838403

Offset

6,2

Links

Table of n, a(n) for n=6..32.

Words built with 0,1,2

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

Formula

G.f.: x^6*(x+1)*(x^2+x+1)*(x^2-x+1)*(x^4+x^3+x^2+x+1) / ((2*x^5+2*x^4 +2*x^3 +2*x^2+2*x-1) * (x^10+3*x^9+5*x^8+7*x^7+9*x^6+9*x^5 +7*x^4 +5*x^3 +3*x^2+x-1)).

Mathematica

Drop[CoefficientList[Series[x^6 (x + 1) (x^2 + x + 1) (x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)/((2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x - 1) (x^10 + 3 x^9 + 5 x^8 + 7 x^7 + 9 x^6 + 9 x^5 + 7 x^4 + 5 x^3 + 3 x^2 + x - 1)), {x, 0, 32}], x], 6] (* Michael De Vlieger, Mar 08 2016 *)

Crossrefs

Cf. A081038, A269914, A269915, A269916.

Sequence in context: A231430 A269916 A273205 * A081038 A273389 A153008

Adjacent sequences: A269914 A269915 A269916 * A269918 A269919 A269920

Keyword

nonn

Author

Marko Riedel, Mar 07 2016

Status

approved