|
|
A218475
|
|
Number of 3n-length 5-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.
|
|
2
|
|
|
1, 1, 13, 217, 4085, 82593, 1751197, 38413481, 864413317, 19842830065, 462825376685, 10937407206265, 261311076852245, 6301225556698177, 153160687795008445, 3748598210810053449, 92303640047399410341, 2285025852515378528913, 56836898766186234593485
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*4^j for n>0, a(0) = 1.
Recurrence: n*(2*n-1)*(4*n-5)*a(n) = (1216*n^3 - 2452*n^2 + 1267*n - 120)*a(n-1) - 750*(3*n-5)*(3*n-4)*(4*n-1)*a(n-2). - Vaclav Kotesovec, Aug 31 2014
a(n) ~ 4 * 3^(3*n+1/2) / (49 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014
|
|
MAPLE
|
a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*4^j, j=0..n-1)/n):
seq(a(n), n=0..20);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|