A116710 - OEIS

%I #16 Oct 23 2017 19:56:26

%S 1,2,6,22,86,337,1299,4910,18228,66640,240550,859295,3043525,10705182,

%T 37441618,130351650,452119862,1563402141,5392828631,18564966510,

%U 63807048144,219015409556,750968486726,2572756726459,8808011192329,30138217809470,103077794599470

%N Number of permutations of length n which avoid the patterns 1423, 3421.

%H Colin Barker, <a href="/A116710/b116710.txt">Table of n, a(n) for n = 1..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_07">Index entries for linear recurrences with constant coefficients</a>, signature (11,-47,99,-109,63,-18,2).

%F G.f.: x*(1 - 9*x + 31*x^2 - 49*x^3 + 37*x^4 - 14*x^5 + 2*x^6) / ((1 - x)*(1 - 3*x + x^2)^2*(1 - 4*x + 2*x^2)).

%o (PARI) Vec(x*(1 - 9*x + 31*x^2 - 49*x^3 + 37*x^4 - 14*x^5 + 2*x^6) / ((1 - x)*(1 - 3*x + x^2)^2*(1 - 4*x + 2*x^2)) + O(x^30)) \\ _Colin Barker_, Oct 23 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006