

A214613


Abelian complexity function of ordinary paperfolding word (A014707).


1



2, 3, 4, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 5, 4, 3, 4, 5, 6, 5, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 4, 3, 4, 5, 6, 5, 6, 7, 6, 5, 6, 7, 8, 7, 6, 7, 6, 5, 6, 7, 6, 5, 6, 7, 6, 5, 6, 7, 6, 5, 6, 5, 4, 3, 4, 5, 6, 5, 6, 7, 6, 5, 6, 7, 8, 7, 6, 7, 6, 5, 6, 7
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OFFSET

1,1


COMMENTS

k first appears at position A005578(k1).  Charlie Neder, Mar 03 2019


LINKS

Charlie Neder, Table of n, a(n) for n = 1..1024
Blake Madill, Narad Rampersad, The abelian complexity of the paperfolding word, Discrete Math. 313 (2013), no. 7, 831838. MR3017968.


FORMULA

From Charlie Neder, Mar 03 2019: (Start)
Madill and Rampersad provide the following recurrence:
a(1) = 2,
a(4n) = a(2n),
a(4n+2) = a(2n+1) + 1,
a(16n+1) = a(8n+1),
a(16n+{3,7,9,13}) = a(2n+1) + 2,
a(16n+5) = a(4n+1) + 1,
a(16n+11) = a(4n+3) + 1,
a(16n+15) = a(2n+2) + 1. (End)


CROSSREFS

Cf. A014707, A014577.
Sequence in context: A081399 A221108 A205554 * A114524 A058033 A216197
Adjacent sequences: A214610 A214611 A214612 * A214614 A214615 A214616


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 08 2013


EXTENSIONS

a(21)a(82) from Charlie Neder, Mar 03 2019


STATUS

approved



