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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

k first appears at position A005578(k-1). - 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, 831--838. 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

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Last modified August 17 11:14 EDT 2019. Contains 326057 sequences. (Running on oeis4.)