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

Author

Marko Riedel, Mar 07 2016

Keywords

• nonn

Links

• 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,-9,-21,-41,-59,-69,-71,-65,-50,-32,-18,-8,-2).

Crossrefs

Cf. A081038, A269914, A269915, A269916.

Programs

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 *)

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)).