cp's OEIS Frontend

A295873 Number of permutations of length n which avoid the patterns 1342, 2413, 3124 and 3142.

%I A295873 #15 Dec 27 2017 08:02:17
%S A295873 1,1,2,6,20,68,231,781,2629,8821,29530,98706,329592,1099792,3668127,
%T A295873 12230505,40771337,135895689,452914658,1509385902,5029980252,
%U A295873 16761785436,55855539047,186125915029,620217261197,2066704787645,6886704234970,22947920663130,76467083518464
%N A295873 Number of permutations of length n which avoid the patterns 1342, 2413, 3124 and 3142.
%H A295873 Colin Barker, <a href="/A295873/b295873.txt">Table of n, a(n) for n = 0..1000</a>
%H A295873 Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, <a href="https://arxiv.org/abs/1705.04109">Automatic discovery of structural rules of permutation classes</a>, arXiv:1705.04109 [math.CO], 2017.
%H A295873 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,14,-5,1).
%F A295873 G.f.: (1-6*x+11*x^2-6*x^3+x^4)/(1-7*x+16*x^2-14*x^3+5*x^4-x^5).
%F A295873 From _Colin Barker_, Dec 27 2017: (Start)
%F A295873 G.f.: (1 - 3*x + x^2)^2 / ((1 - x)*(1 - 6*x + 10*x^2 - 4*x^3 + x^4)).
%F A295873 a(n) = 7*a(n-1) - 16*a(n-2) + 14*a(n-3) - 5*a(n-4) + a(n-5) for n>4.
%F A295873 (End)
%o A295873 (PARI) Vec((1 - 3*x + x^2)^2 / ((1 - x)*(1 - 6*x + 10*x^2 - 4*x^3 + x^4)) + O(x^40)) \\ _Colin Barker_, Dec 27 2017
%K A295873 nonn,easy
%O A295873 0,3
%A A295873 _Bjarki Ágúst Guðmundsson_, Dec 26 2017