cp's OEIS Frontend

A212418 Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> acb <--> cba where a

%I A212418 #23 Aug 03 2018 19:35:52
%S A212418 1,1,1,3,9,54,285,2160,15825,151200,1411095,16329600,185067855,
%T A212418 2514758400,33530101605,523069747200,8020402655265,141228831744000,
%U A212418 2447966414868975,48017802792960000,928344187296100575,20071441567457280000,428190753438433910925
%N A212418 Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> acb <--> cba where a<b<c.
%C A212418 Also size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> bac <--> cba where a<b<c.
%H A212418 Alois P. Heinz, <a href="/A212418/b212418.txt">Table of n, a(n) for n = 0..450</a>
%H A212418 Steven Linton, James Propp, Tom Roby, and Julian West, <a href="http://arxiv.org/abs/1111.3920">Equivalence classes of permutations under various relations generated by constrained transpositions, 2011</a> arXiv:1111.3920 [math.CO]
%F A212418 a(n) = 1 for n<3, otherwise: a(2k+1) = (3/2)*k*(k+1)*(2k-1)!, a(2k) = (3/2)*k*(k-1/3)*(2k-2)!-(2k-3)!!.
%e A212418 From _Alois P. Heinz_, May 21 2012: (Start)
%e A212418 a(3) = 3: {123, 132, 321}.
%e A212418 a(4) = 9: {1234, 1243, 1324, 1342, 1423, 1432, 3214, 4213, 4312}. (End)
%p A212418 a:= proc(n) local k;
%p A212418        k:= iquo(n, 2, 'r');
%p A212418       `if`(n<3, 1, `if`(r=0, (3/2)*k*(k-1/3)*(2*k-2)!
%p A212418        -doublefactorial(2*k-3), (3/2)*k*(k+1)*(2*k-1)!))
%p A212418     end:
%p A212418 seq(a(n), n=0..30);  # _Alois P. Heinz_, May 20 2012
%t A212418 a[n_ /; n < 3] = 1;
%t A212418 a[n_?OddQ] := With[{k = (n - 1)/2}, (3/2)*k*(k + 1)*(2 k - 1)!];
%t A212418 a[n_?EvenQ] := With[{k = n/2}, (3/2)*k*(k - 1/3)*(2 k - 2)! - (2 k - 3)!!];
%t A212418 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 07 2017 *)
%Y A212418 Cf. A210669.
%K A212418 nonn
%O A212418 0,4
%A A212418 _Tom Roby_, May 15 2012