%I
%S 1,3,9,25,69,195,555,1573,4457,12677,36165,103323,295639,847587,
%T 2434755,7006089,20193261,58296927,168567687,488155597,1415686337,
%U 4111268669,11955274925,34808988199,101471734355,296139036809,865204909777,2530413173787,7407817001559,21706686476055,63662015359655
%N a(n) = number of nlettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 2, 1] as of [1, 3, 1].
%H Alois P. Heinz, <a href="/A211297/b211297.txt">Table of n, a(n) for n = 0..1000</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 07 2012
