A211029 Triangle read by rows in which row n lists the binary words of length n over the alphabet {1,2} with no initial repeats.

1, 2, 12, 21, 121, 122, 211, 212, 1211, 1221, 1222, 2111, 2112, 2122, 12111, 12112, 12211, 12212, 12221, 12222, 21111, 21112, 21121, 21122, 21221, 21222, 121111, 121112, 121122, 122111, 122112, 122121, 122211, 122212, 122221, 122222, 211111, 211112

Offset: 1

Author

Omar E. Pol, Nov 29 2012

Keywords

• nonn
• tabf

Comments

As usual in the OEIS, binary alphabets are encoded with {1,2} over the alphabet {0,1} the entries contain nonzero "numbers" beginning with 0.

Examples

			The fourth row of triangle of binary sequences is
0100, 0110, 0111, 1000, 1001, 1011 (see section example of A122536) therefore the fourth row of this triangle is
1211, 1221, 1222, 2111, 2112, 2122.
The first six rows of triangle are:
1, 2;
12, 21;
121, 122, 211, 212;
1211, 1221, 1222, 2111, 2112, 2122;
12111, 12112, 12211, 12212, 12221, 12222, 21111, 21112, 21121, 21122, 21221, 21222;
121111, 121112, 121122, 122111, 122112, 122121, 122211, 122212, 122221, 122222, 211111, 211112, 211121, 211122, 211212, 211221, 211222, 212211, 212221, 212222;
		

Links

• Alois P. Heinz, Rows n = 1..14, flattened
• Index entries for sequences related to curling numbers

Crossrefs

Row n has length A122536(n).

Cf. A093371, A211027, A213969, A216955.

Programs

Maple

s:= proc(n) s(n):= `if`(n=0, [[]], map(x->
      [[x[], 1], [x[], 2]][], s(n-1))) end:
T:= proc(n) map(x-> parse(cat(x[])), select(proc(l) local i;
      for i to iquo(nops(l), 2) do if l[1..i]=l[i+1..2*i]
      then return false fi od; true end, s(n)))[] end:
seq(T(n), n=1..7);  # Alois P. Heinz, Dec 02 2012

Extensions

More terms and name improved by R. J. Mathar, Nov 30 2012