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A212432 Number of equivalence classes of S_n under transformations of positionally and numerically adjacent elements of the form abc <--> acb <--> cba where a<b<c. 0
1, 1, 2, 4, 16, 84, 536, 3912, 32256, 297072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also number of equivalence classes of S_n under transformations of positionally and numerically adjacent elements of the form abc <--> bac <--> cba where a < b < c.

LINKS

Table of n, a(n) for n=0..9.

S. Linton, J. Propp, T. Roby, and J. West, Equivalence Classes of Permutations under Various Relations Generated by Constrained Transpositions, arXiv:1111.3920, 2011 [math.CO], J. Int. Seq. 15 (2012) #12.9.1

EXAMPLE

From Alois P. Heinz, Jun 22 2012: (Start)

a(3) = 4: {123, 132, 321}, {213}, {231}, {312}.

a(4) = 16: {1234, 1243, 1324, 1432, 3214}, {1342}, {1423}, {2134}, {2143}, {2314}, {2341, 2431, 4123, 4132, 4321}, {2413}, {3124}, {3142}, {3241}, {3412}, {3421}, {4213}, {4231}, {4312}.

a(5) = 84: {12345, 12354, 12435, 12543, 13245, 13254, 14325, 32145, 32154}, {12453}, ..., {53421}, {54213}, {54231}.

(End)

CROSSREFS

Cf. A212581.

Sequence in context: A000090 A295922 A300100 * A013115 A291286 A007171

Adjacent sequences:  A212429 A212430 A212431 * A212433 A212434 A212435

KEYWORD

nonn,more

AUTHOR

Tom Roby, Jun 21 2012

EXTENSIONS

a(9) from Alois P. Heinz, Jun 23 2012

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)