A321037 - OEIS

A321037

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

%I #4 Oct 26 2018 16:25:42

%S 7752,942172,69858360,4110110550,211675627240,10018481786544,

%T 448004505210535,19256258184412314,804574034878107648,

%U 32931600573236529164,1327621591399983233480,52924527085674622431690,2092267882428782767625532,82204203906811813227807616

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

%H Alois P. Heinz, <a href="/A321037/b321037.txt">Table of n, a(n) for n = 7..627</a>

%p b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):

%p a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(7):

%p seq(a(n), n=7..25);

%Y Column k=7 of A256311.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Oct 26 2018