cp's OEIS Frontend

A194716 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting four doublets into the initially empty word.

%I A194716 #11 Jul 13 2015 19:06:56
%S A194716 0,1,35,181,523,1145,2131,3565,5531,8113,11395,15461,20395,26281,
%T A194716 33203,41245,50491,61025,72931,86293,101195,117721,135955,155981,
%U A194716 177883,201745,227651,255685,285931,318473,353395,390781,430715,473281,518563,566645,617611
%N A194716 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting four doublets into the initially empty word.
%H A194716 Alois P. Heinz, <a href="/A194716/b194716.txt">Table of n, a(n) for n = 0..1000</a>
%F A194716 G.f.: x*(1+31*x+47*x^2+5*x^3) / (x-1)^4.
%F A194716 a(0) = 0, a(n) = 1+(6+(14+14*(n-1))*(n-1))*(n-1) for n>0.
%e A194716 a(2) = 35: aaaaaaaa, aaaaaabb, aaaaabba, aaaabaab, aaaabbaa, aaaabbbb, aaabaaba, aaabbaaa, aaabbabb, aaabbbba, aabaaaab, aabaabaa, aabaabbb, aababbab, aabbaaaa, aabbaabb, aabbabba, aabbbaab, aabbbbaa, aabbbbbb, abaaaaba, abaabaaa, abaababb, abaabbba, ababbaba, abbaaaaa, abbaaabb, abbaabba, abbabaab, abbabbaa, abbabbbb, abbbaaba, abbbbaaa, abbbbabb, abbbbbba (with 2-ary alphabet {a,b}).
%p A194716 a:= n-> `if`(n=0, 0, (x-> 1+(6+(14+14*x)*x)*x)(n-1)):
%p A194716 seq(a(n), n=0..40);
%Y A194716 Row n=4 of A183134.
%K A194716 nonn
%O A194716 0,3
%A A194716 _Alois P. Heinz_, Sep 02 2011