

A218475


Number of 3nlength 5ary 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
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OFFSET

0,3


LINKS



FORMULA

a(n) = 1/n * Sum_{j=0..n1} C(3*n,j)*(nj)*4^j for n>0, a(0) = 1.
Recurrence: n*(2*n1)*(4*n5)*a(n) = (1216*n^3  2452*n^2 + 1267*n  120)*a(n1)  750*(3*n5)*(3*n4)*(4*n1)*a(n2).  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)*(nj)*4^j, j=0..n1)/n):
seq(a(n), n=0..20);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



