%I
%S 1,3,9,28,86,265,816,2513,7739,23833,73396,226030,696081,2143648,
%T 6601569,20330163,62608681,192809420,593775046,1828587033,5631308624,
%U 17342153393,53406819691,164471408185,506505428836,1559831901918
%N Length of lists created by n substitutions k > Range[0,1+Mod[k+1,3]] starting with {0}.
%C Transformation invert T109 gave a match with A078039; T100 binomial gave a match with A012781; equivalent to replacements 0>{0,1,2}; 1>{0,1,2,3}; 2>{0,1}, 3>{0,1,2} operating n times with {0}.
%H Tomislav Doslic, I. Zubac, <a href="http://amcjournal.eu/index.php/amc/article/view/851">Counting maximal matchings in linear polymers</a>, Ars Mathematica Contemporanea 11 (2016) 255276.
%F G.f.: (1+x)/(12x3x^2x^3).
%F a(n) = A000931(4*n + 6).  _Michael Somos_, Sep 18 2012
%e {0}, {0,1,2}, {0,1,2,0,1,2,3,0,1}, {0,1,2,0,1,2,3,0,1,0,1,2,0,1,2,3,0,1,0,1,2,0,1,2,0,1,2,3} have lengths 1, 3, 9, 28.
%e 1 + 3*x + 9*x^2 + 28*x^3 + 86*x^4 + 265*x^5 + 816*x^6 + ...
%t Length/@Flatten/@NestList[ # /. k_Integer:>Range[0, 1+Mod[k+1, 3]]&, {0}, 8]
%Y Cf. A000931, A078039, A012781.
%K nonn
%O 0,2
%A _Wouter Meeussen_, May 11 2003
