A107638 - OEIS

%I #7 Mar 20 2024 04:46:57

%S 1,1,1,3,1,3,4,1,3,4,1,3,4,6,1,3,4,6,1,3,4,6,8,1,3,4,6,8,9,1,3,4,6,8,

%T 9,1,3,4,6,8,9,11,1,3,4,6,8,9,11,12,1,3,4,6,8,9,11,12,1,3,4,6,8,9,11,

%U 12,14,1,3,4,6,8,9,11,12,14,1,3,4,6,8,9,11,12,14,16,1,3,4,6,8,9,11,12,14

%N Order of appearance of ones in the Fibonacci substitution :triangular in form.

%C Fibonacci substitutions contain three types of information: 1) length 2) count of ones and twos 3) order of appearance of ones and twos

%F 1->{1, 2}, (Correction) 2->{1}

%e 1

%e 1

%e 1,3

%e 1,3,4

%e 1,3,4

%e 1,3,4,6

%e 1,3,4,6,

%e 1,3,4,6,8

%e 1,3,4,6,8,9

%t s[1] = {1, 2}; s[2] = {1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; a = Table[Flatten[Table[If[p[i][[j]] == 1, j, {}], {j, 1, i}]], {i, 1, 20}]

%Y Cf. A000045.

%K nonn,uned,tabf

%O 0,4

%A _Roger L. Bagula_, Jun 09 2005