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

0,3

References

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

Links

Table of n, a(n) for n=0..25.

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]

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 *)

Crossrefs

Sequence in context: A340257 A261386 A073388 * A026126 A026155 A025182

Adjacent sequences: A109631 A109632 A109633 * A109635 A109636 A109637

Keyword

nonn

Author

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

Extensions

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

Status

approved