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A214613
Abelian complexity function of ordinary paperfolding word (A014707).
3
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 08 2013
EXTENSIONS
a(21)-a(82) from Charlie Neder, Mar 03 2019
STATUS
approved