A280318 a(n) is the n-th permutation generated by Heap's algorithm, represented by row number of A055089.

0, 1, 3, 2, 4, 5, 11, 10, 8, 9, 7, 6, 12, 13, 15, 14, 16, 17, 23, 22, 20, 21, 19, 18, 93, 92, 94, 95, 90, 91, 78, 79, 81, 80, 82, 83, 89, 88, 86, 87, 85, 84, 74, 75, 73, 72, 77, 76, 52, 53, 48, 49, 51, 50, 71, 70, 68, 69, 67, 66, 55, 54, 59, 58

Offset: 0

Author

Tilman Piesk, Dec 31 2016

Keywords

• nonn
• tabf

Comments

This is a permutation of the nonnegative integers. It divides naturally in sections of factorial length, so it can be seen as a triangle with row lengths A094258:

0,

1,

3, 2, 4, 5,

11, 10, 8, 9, 7, 6, 12, 13, 15, 14, 16, 17, 23, 22, 20, 21, 19, 18...

Compare A280319 for Steinhaus-Johnson-Trotter algorithm, which is a triangle of finite permutations rather than one infinite permutation.

Examples

			Example for the first 24 entries of the sequence. On the right are the permutations of {1,2,3,4} in the order generated by the Heap's algorithm:
   n    rev colex        a(n)   Heap's
   0     1 2 3 4          0     1 2 3 4
   1     2 1 3 4          1     2 1 3 4
   2     1 3 2 4          3     3 1 2 4
   3     3 1 2 4          2     1 3 2 4
   4     2 3 1 4          4     2 3 1 4
   5     3 2 1 4          5     3 2 1 4
   6     1 2 4 3         11     4 2 1 3
   7     2 1 4 3         10     2 4 1 3
   8     1 4 2 3          8     1 4 2 3
   9     4 1 2 3          9     4 1 2 3
  10     2 4 1 3          7     2 1 4 3
  11     4 2 1 3          6     1 2 4 3
  12     1 3 4 2         12     1 3 4 2
  13     3 1 4 2         13     3 1 4 2
  14     1 4 3 2         15     4 1 3 2
  15     4 1 3 2         14     1 4 3 2
  16     3 4 1 2         16     3 4 1 2
  17     4 3 1 2         17     4 3 1 2
  18     2 3 4 1         23     4 3 2 1
  19     3 2 4 1         22     3 4 2 1
  20     2 4 3 1         20     2 4 3 1
  21     4 2 3 1         21     4 2 3 1
  22     3 4 2 1         19     3 2 4 1
  23     4 3 2 1         18     2 3 4 1
		

Links

• Tilman Piesk, Table of n, a(n) for n = 0..5039
• Tilman Piesk, Calculation in Python
• Wikipedia, Heap's algorithm

Crossrefs

Cf. A055089, A094258, A280319.