cp's OEIS Frontend

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.

%I A321032 #7 Oct 26 2018 14:58:23
%S A321032 3,18,97,530,2973,17059,99657,590562,3540463,21430266,130771375,
%T A321032 803538099,4967127735,30866224823,192696614729,1207967820098,
%U A321032 7600482116931,47981452358200,303820299643137,1929099000980218,12279621792772821,78346444891033855
%N 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.
%H A321032 Alois P. Heinz, <a href="/A321032/b321032.txt">Table of n, a(n) for n = 2..1211</a>
%e A321032 a(2) = 3: aaabbb, aabbba, abbbaa.
%e A321032 a(3) = 18: aaaaaabbb, aaaaabbba, aaaabbbaa, aaabaaabb, aaabbaaab, aaabbbaaa, aaabbbbbb, aabaaabba, aabbaaaba, aabbbaaaa, aabbbabbb, aabbbbbba, abaaabbaa, abbaaabaa, abbbaaaaa, abbbaabbb, abbbabbba, abbbbbbaa.
%p A321032 b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
%p A321032 a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(2):
%p A321032 seq(a(n), n=2..25);
%Y A321032 Column k=2 of A256311.
%K A321032 nonn
%O A321032 2,1
%A A321032 _Alois P. Heinz_, Oct 26 2018