A321032 Number of words of length 3n such that all letters of the binary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples into the initially empty word.

3, 18, 97, 530, 2973, 17059, 99657, 590562, 3540463, 21430266, 130771375, 803538099, 4967127735, 30866224823, 192696614729, 1207967820098, 7600482116931, 47981452358200, 303820299643137, 1929099000980218, 12279621792772821, 78346444891033855

Offset

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1211

Example

a(2) = 3: aaabbb, aabbba, abbbaa.
a(3) = 18: aaaaaabbb, aaaaabbba, aaaabbbaa, aaabaaabb, aaabbaaab, aaabbbaaa, aaabbbbbb, aabaaabba, aabbaaaba, aabbbaaaa, aabbbabbb, aabbbbbba, abaaabbaa, abbaaabaa, abbbaaaaa, abbbaabbb, abbbabbba, abbbbbbaa.

Maple

b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(2):
seq(a(n), n=2..25);

Crossrefs

Column k=2 of A256311.

Sequence in context: A129547 A081151 A132848 * A180036 A038158 A327828

Adjacent sequences: A321029 A321030 A321031 * A321033 A321034 A321035

Keyword

nonn

Author

Alois P. Heinz, Oct 26 2018

Status

approved