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A218474 Number of 3n-length 4-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, 10, 127, 1810, 27631, 441604, 7293700, 123485914, 2131511455, 37368531010, 663539143015, 11908626395320, 215670579863428, 3936425910379840, 72335601620713432, 1337149262553687658, 24847762997547701695, 463900901255209923310, 8697278488612398979645 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

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

a(n) ~ 3^(4*n+3/2) / (25*sqrt(Pi)*n^(3/2)*4^n). - Vaclav Kotesovec, Jul 16 2014

MAPLE

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

seq(a(n), n=0..20);

# second Maple program:

a:= proc(n) option remember; `if`(n<3, [1, 1, 10][n+1],

      ((2359*n^3 -5063*n^2 +2898*n -360)*a(n-1)

       -576*(3*n-5)*(7*n-2)*(3*n-4)*a(n-2))/

       (2*(2*n-1)*(7*n-9)*n))

    end:

seq(a(n), n=0..30);

CROSSREFS

Column k=4 of A213027.

Sequence in context: A079241 A270965 A245923 * A234284 A296379 A183538

Adjacent sequences:  A218471 A218472 A218473 * A218475 A218476 A218477

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 29 2012

STATUS

approved

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Last modified November 16 23:51 EST 2018. Contains 317275 sequences. (Running on oeis4.)