A109634 Number of 1's that appear among all ternary strings of length n that contain no consecutive 1's.

0, 1, 4, 16, 56, 188, 608, 1920, 5952, 18192, 54976, 164608, 489088, 1443776, 4238336, 12382208, 36022272, 104407296, 301618176, 868765696, 2495715328, 7152286720, 20452548608, 58369409024, 166276481024, 472876388352

Offset: 0

Author

Ralph P. Grimaldi (ralph.grimaldi(AT)rose-hulman.edu), Aug 03 2005

Keywords

• nonn

References

• Ralph P. Grimaldi, Ternary Strings with No Consecutive 1's, Ars Combin. 89 (2008), 321-343.

Programs

Mathematica

f[n_] := Simplify[(2Sqrt[3] (-(1 - Sqrt[3])^n + (1 + Sqrt[3])^n) + 3n*((1 - Sqrt[3])^(1 + n) + (1 + Sqrt[3])^(1 + n)))/36]; Table[ f[n], {n, 0, 25}] (* Robert G. Wilson v *)

Formula

(sqrt(3)/18)*((1+sqrt(3))^n - (1-sqrt(3))^n)+(n/12)*((1+sqrt(3))^(n+1)+(1-sqrt(3))^(n+1))

Conjecture: a(n)=A073388(n-1). [From R. J. Mathar, Aug 18 2008]

Extensions

More terms from Robert G. Wilson v, Aug 05 2005