A214613 Abelian complexity function of ordinary paperfolding word (A014707).

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

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 [Corrected by Kevin Ryde, Sep 05 2020]: (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) + 2,

a(16n+11) = a(4n+3) + 2,

a(16n+15) = a(2n+2) + 1. (End)

Crossrefs

Cf. A014707, A014577, A005578, A337120.

Sequence in context: A373579 A336750 A336755 * A364801 A325933 A114524

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