A287561 - OEIS

%I #4 May 31 2017 16:14:54

%S 0,2,1,3,1,3,0,2,2,1,3,0,3,0,2,1,2,1,3,0,3,0,2,1,0,2,1,3,1,3,0,2,1,3,

%T 0,2,2,1,3,0,3,0,2,1,0,2,1,3,3,0,2,1,0,2,1,3,1,3,0,2,2,1,3,0,1,3,0,2,

%U 2,1,3,0,3,0,2,1,0,2,1,3,3,0,2,1,0,2

%N Start with 0 and repeatedly substitute 0->0213, 1->2130, 2->1302, 3->3021.

%C This is the fixed point of the morphism 0->0213, 1->2130, 2->1302, 3->3021 starting with 0.  Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4,  w(n)/n -> 4.   Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1.  See A287556 for a guide to related sequences.

%H Clark Kimberling, <a href="/A287561/b287561.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F a(n) = 4n - A287565(n) for n >= 1.

%e First three iterations of the morphism:

%e 0213

%e 0213130221303021

%e 0213130221303021213030210213130213022130302102133021021313022130

%t s = Nest[Flatten[# /. {0 -> {0, 2, 1, 3}, 1 -> {2, 1, 3, 0}, 2 -> {1, 3, 0, 2}, 3 -> {3, 0, 2, 1}}] &, {0}, 9];   (* A287561 *)

%t Flatten[Position[s, 0]]; (* A287562 *)

%t Flatten[Position[s, 1]]; (* A287563 *)

%t Flatten[Position[s, 2]]; (* A287564 *)

%t Flatten[Position[s, 3]]; (* A287565 *)

%Y Cf. A287562, A287563, A287564, A287565.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 31 2017