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A084084 Length of lists created by n substitutions k -> Range[0,1+Mod[k+1,3]] starting with {0}. 0

%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://amc-journal.eu/index.php/amc/article/view/851">Counting maximal matchings in linear polymers</a>, Ars Mathematica Contemporanea 11 (2016) 255-276.

%F G.f.: (1+x)/(1-2x-3x^2-x^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

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)