A368804 Irregular triangle read by rows: T(n,k) is the k-th balanced binary word of length 2*n, where words within a row are in lexicographical order (with leading zeros removed and interpreted as decimal numbers).

1, 10, 11, 101, 110, 1001, 1010, 1100, 111, 1011, 1101, 1110, 10011, 10101, 10110, 11001, 11010, 11100, 100011, 100101, 100110, 101001, 101010, 101100, 110001, 110010, 110100, 111000, 1111, 10111, 11011, 11101, 11110, 100111, 101011, 101101, 101110, 110011, 110101, 110110

Offset: 1

Author

Paolo Xausa, Jan 06 2024

Keywords

• nonn
• tabf
• base
• easy

Comments

A balanced binary word is composed of the same number of zeros and ones.

This is triangle A362030 with terms converted to binary and interpreted as decimal numbers.

Examples

			Triangle begins (where terms in row n are padded with zeros on the left to form a 2*n word):
  [1] 01 10;
  [2] 0011 0101 0110 1001 1010 1100;
  [3] 000111 001011 001101 001110 010011 010101 010110 011001 011010 011100 ... ;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..17576 (rows 1..8 of the triangle, flattened).

Crossrefs

Cf. A014486, A063171, A362030.

Cf. A368750, A368751, A368752, A368753.

Programs

Mathematica

words[n_]:=Permutations[PadLeft[PadLeft[{},n,1],2n]];
Array[Map[FromDigits,words[#]]&,4]