login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 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,

%T 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,

%U 3,1,2,4,3,2,1,3,4,2,1,3,2,4,1,3,2,1,4

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

%C 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

%H R. J. Cano, <a href="/A207324/b207324.txt">Table of n, a(n) for n = 1..10000</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/demo/comb/#perm-trotter">C programs related to this sequence</a>

%H R. J. Cano, <a href="/wiki/User:R._J._Cano/Permutation_Sequences"> Sequencer programs and additional information</a>

%H Selmer M. Johnson, <a href="https://doi.org/10.1090/S0025-5718-1963-0159764-2">Generation of permutations by adjacent transposition</a>, Mathematics of Computation, 17 (1963), p. 282-285.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Steinhaus%E2%80%93Johnson%E2%80%93Trotter_algorithm">Steinhaus-Johnson-Trotter algorithm</a>

%H <a href="/index/Per#perm">Index entries for sequences related to permutations</a>

%e 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.

%e 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.

%e Up to N concatenations, the sequence will have a total of Sum_{k=1..N} (k! * k) = (N+1)! - 1 = A033312(N+1) terms.

%Y Cf. A030298, A055881.

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

%Y 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.

%K nonn,easy,tabf

%O 1,3

%A _R. J. Cano_, Sep 14 2012

%E Edited by _N. J. A. Sloane_, _Antti Karttunen_ and _R. J. Cano_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 13:28 EST 2019. Contains 329916 sequences. (Running on oeis4.)