A316329 - OEIS

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A316329

Image of 3 under repeated applications of the morphism 1 -> 11, 2 -> 2, 3 -> 312.

3, 312, 312112, 31211211112, 31211211112111111112, 3121121111211111111211111111111111112, 3121121111211111111211111111111111112111111111111111111111111111111112

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OFFSET

0,1

COMMENTS

a(n) has length 2^n + n.

REFERENCES

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, Problem 4, p. 242.

LINKS

Table of n, a(n) for n=0..6.

MAPLE

b:= proc(n) option remember; `if`(n=0, 3, (l-> subs(3=

[3, 1, 2][], subs(1=[1$2][], l))[])([b(n-1)])) end:

a:= n-> parse(cat(b(n))):

seq(a(n), n=0..6); # Alois P. Heinz, May 26 2021

MATHEMATICA

FromDigits /@ SubstitutionSystem[{1 -> {1, 1}, 2 -> {2}, 3 -> {3, 1, 2}}, {3}, 6] (* Jean-François Alcover, May 14 2022 *)

CROSSREFS

Sequence in context: A132305 A074327 A179109 * A062333 A222725 A303893

Adjacent sequences: A316326 A316327 A316328 * A316330 A316331 A316332

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 14 2018

EXTENSIONS

a(2) corrected by Georg Fischer, May 26 2021

STATUS

approved