A207324 List of permutations of 1,2,3,...,n for n=1,2,3,..., in the order they are output by Steinhaus-Johnson-Trotter algorithm.

1, 1, 2, 2, 1, 1, 2, 3, 1, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 4, 1, 2, 4, 3, 1, 4, 2, 3, 4, 1, 2, 3, 4, 1, 3, 2, 1, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 3, 1, 2, 4, 3, 1, 4, 2, 3, 4, 1, 2, 4, 3, 1, 2, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4

Offset

1,3

Comments

This table is otherwise similar to A030298, but lists permutations in the order given by the Steinhaus-Trotter-Johnson algorithm. - Antti Karttunen, Dec 28 2012

Links

R. J. Cano, Table of n, a(n) for n = 1..10000

Joerg Arndt, C programs related to this sequence

R. J. Cano, Sequencer programs and additional information

Selmer M. Johnson, Generation of permutations by adjacent transposition, Mathematics of Computation, 17 (1963), p. 282-285.

Wikipedia, Steinhaus-Johnson-Trotter algorithm

Index entries for sequences related to permutations

Example

For the set of the first two natural numbers {1,2} the unique permutations possible are 12 and 21, concatenated with 1 for {1} the resulting sequence would be 1, 1, 2, 2, 1.
If we consider up to 3 elements {1,2,3}, we have 123, 132, 312, 321, 231, 213 and the concatenation gives: 1, 1, 2, 2, 1, 1, 2, 3, 1, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3.
Up to N concatenations, the sequence will have a total of Sum_{k=1..N} (k! * k) = (N+1)! - 1 = A033312(N+1) terms.

Crossrefs

Cf. A030298, A055881.

Cf. A001563 (row lengths), A001286 (row sums).

Pair (A130664(n),A084555(n)) = (1,1),(2,3),(4,5),(6,8),(9,11),(12,14),... gives the starting and ending offsets of the n-th permutation in this list.

Sequence in context: A030298 A370221 A098281 * A352620 A103343 A085263

Adjacent sequences: A207321 A207322 A207323 * A207325 A207326 A207327

Keyword

nonn,easy,tabf

Author

R. J. Cano, Sep 14 2012

Extensions

Edited by N. J. A. Sloane, Antti Karttunen and R. J. Cano

Status

approved