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A084084 Length of lists created by n substitutions k -> Range[0,1+Mod[k+1,3]] starting with {0}. 0
1, 3, 9, 28, 86, 265, 816, 2513, 7739, 23833, 73396, 226030, 696081, 2143648, 6601569, 20330163, 62608681, 192809420, 593775046, 1828587033, 5631308624, 17342153393, 53406819691, 164471408185, 506505428836, 1559831901918 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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}.

LINKS

Table of n, a(n) for n=0..25.

Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276.

FORMULA

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

a(n) = A000931(4*n + 6). - Michael Somos, Sep 18 2012

EXAMPLE

{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.

1 + 3*x + 9*x^2 + 28*x^3 + 86*x^4 + 265*x^5 + 816*x^6 + ...

MATHEMATICA

Length/@Flatten/@NestList[ # /. k_Integer:>Range[0, 1+Mod[k+1, 3]]&, {0}, 8]

CROSSREFS

Cf. A000931, A078039, A012781.

Sequence in context: A291731 A291257 A005354 * A091140 A052541 A024738

Adjacent sequences:  A084081 A084082 A084083 * A084085 A084086 A084087

KEYWORD

nonn

AUTHOR

Wouter Meeussen, May 11 2003

STATUS

approved

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)