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A084085 Length of lists created by n substitutions k -> Range[0,Mod[k+1,4]] starting with {0}. 0
1, 2, 5, 14, 38, 102, 273, 731, 1958, 5245, 14050, 37636, 100816, 270057, 723405, 1937794, 5190793, 13904642, 37246538, 99772766, 267262553, 715919535, 1917742590, 5137081001, 13760762966, 36861127432, 98740361920, 264497039329 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

equivalent to replacements 0->{0,1}; 1->{0,1,2}; 2->{0,1,2,3}; 3->{0} operating n times with {0}.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

G.f.: -(1-x+x^3)/(-x^2-1+3 x+x^4))

EXAMPLE

{0}, {0,1}, {0,1,0,1,2}, {0,1,0,1,2,0,1,0,1,2,0,1,2,3} have lengths 1, 2, 5, 14.

MATHEMATICA

Length/@Flatten/@NestList[ # /. k_Integer:>Range[0, Mod[k+1, 4]]&, {0}, 8]

CROSSREFS

Sequence in context: A228952 A172259 A292327 * A052985 A052945 A026288

Adjacent sequences:  A084082 A084083 A084084 * A084086 A084087 A084088

KEYWORD

nonn

AUTHOR

Wouter Meeussen, May 11 2003

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)