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

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Column k=2 of A256311.

Programs

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);