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A256181 The number of permutations of length n sortable by 3 block interchanges.

%I A256181 #31 Dec 15 2015 12:08:18
%S A256181 1,2,6,24,120,720,5040,32256,169632,737364,2731444,8875868,25894376,
%T A256181 69053375,170694383,395443223,866147111,1806459866,3608498678,
%U A256181 6937282452,12887902732,23216767894,40675018726,69480583966,115975600846,189528370396,303753983092
%N A256181 The number of permutations of length n sortable by 3 block interchanges.
%H A256181 Colin Barker, <a href="/A256181/b256181.txt">Table of n, a(n) for n = 1..1000</a>
%H A256181 D. A. Christie, <a href="http://dx.doi.org/10.1016/S0020-0190(96)00155-X">Sorting Permutations by Block-Interchanges</a>, Inf. Process. Lett. 60 (1996), 165-169.
%H A256181 C. Homberger, V. Vatter, <a href="http://arxiv.org/abs/1308.4946">On the effective and automatic enumeration of polynomial permutation classes</a>, arXiv preprint arXiv:1308.4946 [math.CO], 2013-2015.
%H A256181 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A256181 G.f.: -x * (x^12 -12*x^11 +66*x^10 -217*x^9 +567*x^8 -270*x^7 +1608*x^6 -541*x^5 +419*x^4 -184*x^3 +58*x^2 -11*x +1) / (x^13 -13*x^12 +78*x^11 -286*x^10 +715*x^9 -1287*x^8 +1716*x^7 -1716*x^6 +1287*x^5 -715*x^4 +286*x^3 -78*x^2 +13*x -1).
%e A256181 The shortest permutations that cannot be sorted by 3 block interchanges are of length 8.
%o A256181 (PARI) Vec(x*(1-11*x+58*x^2-184*x^3+419*x^4-541*x^5+1608*x^6-270*x^7+567*x^8-217*x^9+66*x^10-12*x^11+x^12)/(1-x)^13 + O(x^30)) \\ _Colin Barker_, Dec 15 2015
%Y A256181 Cf. A145126, A228401.
%K A256181 nonn,easy
%O A256181 1,2
%A A256181 _Vincent Vatter_, Apr 03 2015