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.

0, 1, 35, 181, 523, 1145, 2131, 3565, 5531, 8113, 11395, 15461, 20395, 26281, 33203, 41245, 50491, 61025, 72931, 86293, 101195, 117721, 135955, 155981, 177883, 201745, 227651, 255685, 285931, 318473, 353395, 390781, 430715, 473281, 518563, 566645, 617611

Offset: 0

Author

Alois P. Heinz, Sep 02 2011

Keywords

• nonn

Examples

			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}).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Row n=4 of A183134.

Programs

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(6+(14+14*x)*x)*x)(n-1)):
seq(a(n), n=0..40);

Formula

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

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