

A207324


List of permutations of 1,2,3,...,n for n=1,2,3,..., in the order they are output by SteinhausJohnsonTrotter 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
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OFFSET

1,3


COMMENTS

This table is otherwise similar to A030298, but lists permutations in the order given by the SteinhausTrotterJohnson 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. 282285.
Wikipedia, SteinhausJohnsonTrotter 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 nth 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



