|
%I #45 Sep 05 2020 22:22:27
%S 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,
%T 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,
%U 6,7,6,5,6,7,8,7,6,7,6,5,6,7
%N Abelian complexity function of ordinary paperfolding word (A014707).
%C k first appears at position A005578(k-1). - _Charlie Neder_, Mar 03 2019
%H Charlie Neder, <a href="/A214613/b214613.txt">Table of n, a(n) for n = 1..1024</a>
%H Blake Madill, Narad Rampersad, <a href="https://doi.org/10.1016/j.disc.2013.01.005">The abelian complexity of the paperfolding word</a>, Discrete Math. 313 (2013), no. 7, 831--838. MR3017968.
%F From _Charlie Neder_, Mar 03 2019 [Corrected by _Kevin Ryde_, Sep 05 2020]: (Start)
%F Madill and Rampersad provide the following recurrence:
%F a(1) = 2,
%F a(4n) = a(2n),
%F a(4n+2) = a(2n+1) + 1,
%F a(16n+1) = a(8n+1),
%F a(16n+{3,7,9,13}) = a(2n+1) + 2,
%F a(16n+5) = a(4n+1) + 2,
%F a(16n+11) = a(4n+3) + 2,
%F a(16n+15) = a(2n+2) + 1. (End)
%Y Cf. A014707, A014577, A005578, A337120.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Mar 08 2013
%E a(21)-a(82) from _Charlie Neder_, Mar 03 2019
|
