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

Author

N. J. A. Sloane, Mar 08 2013

Keywords

• nonn

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.

Crossrefs

Cf. A014707, A014577, A005578, A337120.

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)

Extensions

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