cp's OEIS Frontend

A194718 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting six doublets into the initially empty word.

%I A194718 #13 Oct 21 2022 21:38:54
%S A194718 0,1,462,7941,48838,185193,530526,1265677,2654646,5060433,8960878,
%T A194718 14964501,23826342,36463801,53972478,77642013,108971926,149687457,
%U A194718 201755406,267399973,349118598,449697801,572229022,720124461,897132918,1107355633,1355262126,1645706037
%N A194718 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting six doublets into the initially empty word.
%H A194718 Alois P. Heinz, <a href="/A194718/b194718.txt">Table of n, a(n) for n = 0..1000</a>
%H A194718 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F A194718 G.f.: x*(1+456*x+5184*x^2+8102*x^3+2055*x^4+42*x^5) / (x-1)^6.
%F A194718 a(0) = 0, a(n) = 1+(10+(44+(110+(165+132*(n-1))*(n-1))*(n-1))*(n-1)) * (n-1) for n>0.
%e A194718 a(1) = 1: aaaaaaaaaaaa (with 1-ary alphabet {a}).
%p A194718 a:= n-> `if`(n=0, 0, (x-> 1+(10+(44+(110+(165+132*x)*x)*x)*x)*x)(n-1)):
%p A194718 seq(a(n), n=0..30);
%t A194718 LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,462,7941,48838,185193,530526},30] (* _Harvey P. Dale_, Oct 23 2015 *)
%Y A194718 Row n=6 of A183134.
%K A194718 nonn,easy
%O A194718 0,3
%A A194718 _Alois P. Heinz_, Sep 02 2011