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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. 2

%I

%S 0,1,35,181,523,1145,2131,3565,5531,8113,11395,15461,20395,26281,

%T 33203,41245,50491,61025,72931,86293,101195,117721,135955,155981,

%U 177883,201745,227651,255685,285931,318473,353395,390781,430715,473281,518563,566645,617611

%N 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 Alois P. Heinz, <a href="/A194716/b194716.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x*(1+31*x+47*x^2+5*x^3) / (x-1)^4.

%F a(0) = 0, a(n) = 1+(6+(14+14*(n-1))*(n-1))*(n-1) for n>0.

%e 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 a:= n-> `if`(n=0, 0, (x-> 1+(6+(14+14*x)*x)*x)(n-1)):

%p seq(a(n), n=0..40);

%Y Row n=4 of A183134.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 02 2011

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Last modified November 25 09:29 EST 2020. Contains 338623 sequences. (Running on oeis4.)