A218476 Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.

1, 1, 16, 331, 7746, 195011, 5153626, 140995716, 3958980906, 113434797571, 3303283462836, 97478710394451, 2908594804576416, 87605427983818356, 2659959016770389896, 81330226479826092536, 2501989790308939894026, 77386492111973937031491, 2405093253522796180052056

Offset: 0

Author

Alois P. Heinz, Oct 29 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=6 of A213027.

Programs

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*5^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Formula

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*5^j for n>0, a(0) = 1.

Recurrence: 2*n*(2*n-1)*(9*n-11)*a(n) = 3*(2997*n^3 - 5769*n^2 + 2754*n - 200)*a(n-1) - 3240*(3*n-5)*(3*n-4)*(9*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(3*n-7/2) * 5^(n+1) / (sqrt(Pi) * n^(3/2) * 4^n). - Vaclav Kotesovec, Aug 31 2014