A116820 - OEIS

%I #14 Nov 08 2017 09:57:59

%S 1,2,6,21,75,264,914,3127,10621,35932,121324,409301,1380417,4655382,

%T 15700590,52954137,178609067,602449564,2032105066,6854506171,

%U 23121097405,77990499392,263072412420,887378656761,2993247393297,10096624106970,34057260581510

%N Number of permutations of length n which avoid the patterns 2341, 3241, 4213.

%H Colin Barker, <a href="/A116820/b116820.txt">Table of n, a(n) for n = 1..1000</a>

%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 [math.CO] (2017), Table 2 No 168 and 169.

%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-23,29,-14,1)

%F G.f.: x*(1 - 6*x + 13*x^2 - 10*x^3 + x^4) / ((1 - x)*(1 - 7*x + 16*x^2 - 13*x^3 + x^4)).

%F a(n) = 8*a(n-1) - 23*a(n-2) + 29*a(n-3) - 14*a(n-4) + a(n-5) for n>5. - _Colin Barker_, Oct 18 2017

%o (PARI) Vec(x*(1 - 6*x + 13*x^2 - 10*x^3 + x^4) / ((1 - x)*(1 - 7*x + 16*x^2 - 13*x^3 + x^4)) + O(x^30)) \\ _Colin Barker_, Oct 18 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006