OFFSET
0,3
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.
LINKS
Tilman Piesk, Table of n, a(n) for n = 0..5039
Tilman Piesk, Calculation in Python
Wikipedia, Heap's algorithm
EXAMPLE
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
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Dec 31 2016
STATUS
approved