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Number of permutations of length n which avoid the patterns 2341, 4312.
1

%I #24 Oct 25 2017 09:31:58

%S 1,1,2,6,22,86,338,1318,5110,19770,76466,295810,1144530,4428622,

%T 17136186,66306722,256565926,992749334,3841316550,14863484902,

%U 57512368162,222536820262,861078033110,3331832349354,12892103081874,49884359171762

%N Number of permutations of length n which avoid the patterns 2341, 4312.

%H Colin Barker, <a href="/A116704/b116704.txt">Table of n, a(n) for n = 0..1000</a>

%H Darla Kremer and Wai Chee Shiu, <a href="http://dx.doi.org/10.1016/S0012-365X(03)00042-6">Finite transition matrices for permutations avoiding pairs of length four patterns</a>, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Enumerations_of_specific_permutation_classes#Classes_avoiding_two_patterns_of_length_4">Permutation classes avoiding two patterns of length 4</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,22,-13,4).

%F G.f.: (x^5-5*x^4+13*x^3-12*x^2+6*x-1) / (4*x^5-13*x^4+22*x^3-17*x^2+7*x-1). (corrected by _Jay Pantone_, Feb 18 2016)

%F a(n) = 7*a(n-1) - 17*a(n-2) + 22*a(n-3) - 13*a(n-4) + 4*a(n-5) for n>6. - _Colin Barker_, Oct 25 2017

%o (PARI) Vec((1 - 6*x + 12*x^2 - 13*x^3 + 5*x^4 - x^5) / (1 - 7*x + 17*x^2 - 22*x^3 + 13*x^4 - 4*x^5) + O(x^30)) \\ _Colin Barker_, Oct 25 2017

%K nonn,easy

%O 0,3

%A _Lara Pudwell_, Feb 26 2006

%E Prepended a(0)=1 by _Joerg Arndt_, Feb 18 2016