A107638 Order of appearance of ones in the Fibonacci substitution :triangular in form.

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, 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, 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

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..94.

Formula

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

Example

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

Mathematica

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}]

Crossrefs

Cf. A000045.

Sequence in context: A030708 A095709 A076152 * A245093 A104765 A308690

Adjacent sequences: A107635 A107636 A107637 * A107639 A107640 A107641

Keyword

nonn,uned,tabf

Author

Roger L. Bagula, Jun 09 2005

Status

approved