A209243 3^n times the expected value of the shortest run of 0's in a length n word on alphabet {0,1,2}.

0, 1, 6, 25, 88, 285, 882, 2661, 7916, 23381, 68850, 202621, 596768, 1760289, 5201854, 15401317, 45682536, 135728009, 403864570, 1203278513, 3589064828, 10715405153, 32017223498, 95730557865, 286392391568, 857187336029

Offset

0,3

References

R. Sedgewick and P. Flajolet, Analysis of Algorithms, Addison and Wesley, 1996, Chapter 7

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

O.g.f.: Sum_{k=1..n} x^k/((1 - 2x)*(1 - 3x + 2x^2 - 2x^(k+1)))

Mathematica

nn=25; a=x^k/(1-x); CoefficientList[Series[Sum[(a+1)/(1-(2x a)/(1-2x))/(1-2x)-1/(1-2x), {k, 1, nn}], {x, 0, nn}], x]

Crossrefs

Cf. A209232.

Sequence in context: A220275 A055585 A099625 * A143628 A056279 A055337

Adjacent sequences: A209240 A209241 A209242 * A209244 A209245 A209246

Keyword

nonn

Author

Geoffrey Critzer, Jan 13 2013

Status

approved