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