A338230 Number of ternary strings of length n that contain at least two 0's and at most one 1.

0, 0, 1, 7, 27, 81, 213, 519, 1207, 2725, 6033, 13179, 28515, 61257, 130861, 278287, 589551, 1244877, 2621097, 5504643, 11533915, 24116785, 50331141, 104857047, 218103207, 452984181, 939523393, 1946156299, 4026531027, 8321498265, 17179868253, 35433479199, 73014442975, 150323854237

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

Formula

a(n) = 2^n + n*2^(n-1) - 2*binomial(n,2) - 2*n - 1.

E.g.f.: exp(x)*(exp(x) - 1 - x)*(1 + x).

G.f.: x^2*(1 - 3*x^2)/((1 - 2*x)^2*(1 - x)^3). - Stefano Spezia, Jan 31 2021

Example

a(4) = 27 since the strings consist of 0000, the 4 permutations of 0001, the 4 permutations of 0002, the 6 permutations of 0022, and the 12 permutations of 0012. The total number of strings is then 1 + 4 + 4 + 6 + 12 = 27.

Mathematica

CoefficientList[Series[Exp[x](Exp[x]-1-x)(1+x), {x, 0, 32}], x]Table[i!, {i, 0, 32}] (* Stefano Spezia, Jan 31 2021 *)

Crossrefs

Cf. A186244, A186314.

Cf. A338229, A338232.

Sequence in context: A266761 A027180 A036597 * A038092 A059823 A339771

Adjacent sequences: A338227 A338228 A338229 * A338231 A338232 A338233

Keyword

nonn,easy

Author

Enrique Navarrete, Jan 30 2021

Status

approved