A194730 Number of 10-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.

1, 1, 19, 442, 11395, 312814, 8960878, 264735892, 8006545891, 246643289830, 7711583225338, 244082045341036, 7805301802531534, 251791585570781452, 8183989442287618300, 267755464909548758440, 8810802978165549384355, 291414010749705281701270

Offset

0,3

Links

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

Formula

G.f.: 9/10 + 9/(5*(8+10*sqrt(1-36*x))).

a(0) = 1, a(n) = 1/n * Sum_{j=0..n-1} C(2*n,j)*(n-j)*9^j for n>0.

a(n) ~ 9 * 36^n / (64 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 07 2014

Example

a(2) = 19: aaaa, aabb, aacc, aadd, aaee, aaff, aagg, aahh, aaii, aajj, abba, acca, adda, aeea, affa, agga, ahha, aiia, ajja (with 10-ary alphabet {a,b,c,d,e,f,g,h,i,j}).

Maple

a:= n-> `if`(n=0, 1, add(binomial (2*n, j) *(n-j) *9^j, j=0..n-1) /n):
seq(a(n), n=0..20);

Crossrefs

Column k=10 of A183134.

Sequence in context: A291644 A108145 A114350 * A012506 A285398 A201798

Adjacent sequences: A194727 A194728 A194729 * A194731 A194732 A194733

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2011

Status

approved