cp's OEIS Frontend

A228396 The number of permutations of length n sortable by 2 reversals.

%I A228396 #30 Mar 31 2025 14:49:55
%S A228396 1,1,2,6,22,63,145,288,516,857,1343,2010,2898,4051,5517,7348,9600,
%T A228396 12333,15611,19502,24078,29415,35593,42696,50812,60033,70455,82178,
%U A228396 95306,109947,126213,144220,164088,185941,209907,236118,264710,295823,329601,366192,405748
%N A228396 The number of permutations of length n sortable by 2 reversals.
%H A228396 C. Homberger, <a href="http://arxiv.org/abs/1410.2657">Patterns in Permutations and Involutions: A Structural and Enumerative Approach</a>, arXiv preprint 1410.2657, 2014.
%H A228396 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, 2013.
%H A228396 G. A. Watterson, W. J. Ewens, T. E. Hall, and A. Morgan, <a href="http://dx.doi.org/10.1016/0022-5193(82)90384-8">The chromosome inversion problem</a>, Journal of Theoretical Biology, 99 (1982), 1-7.
%H A228396 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A228396 G.f.: -(x^7 - x^6 - 3*x^5 + 7*x^4 - 4*x^3 + 7*x^2 - 4*x + 1)/(x - 1)^5.
%F A228396 a(n) = 8 + n*(n^3 -2*n^2 +2*n -19)/6 for n>2, a(1)=1, a(2)=2. [_Bruno Berselli_, Aug 22 2013]
%e A228396 There are 2 permutations of length 4 which cannot be sorted by 2 reversals.
%t A228396 CoefficientList[Series[(1/x) (-1 - (x^7 - x^6 - 3 x^5 + 7 x^4 - 4 x^3 + 7 x^2 - 4 x + 1)/(x - 1)^5), {x, 0, 40}], x] (* _Bruno Berselli_, Aug 22 2013 *)
%t A228396 LinearRecurrence[{5,-10,10,-5,1},{1,2,6,22,63,145,288},40] (* _Harvey P. Dale_, Mar 08 2019 *)
%Y A228396 Cf. A000124, A228397.
%K A228396 nonn,easy
%O A228396 0,3
%A A228396 _Vincent Vatter_, Aug 21 2013
%E A228396 a(0)=1 prepended by _Alois P. Heinz_, Mar 31 2025