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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A182592 A030298 A098281 * A103343 A085263 A115092

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

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Last modified November 19 03:27 EST 2019. Contains 329310 sequences. (Running on oeis4.)