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A280318 a(n) is the n-th permutation generated by Heap's algorithm, represented by row number of A055089. 2
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 (list; graph; refs; listen; history; text; internal format)
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, 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
Sequence in context: A334792 A255167 A264993 * A353659 A246982 A258215
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Dec 31 2016
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)