A116707 - OEIS

%I #17 Sep 04 2022 22:17:23

%S 1,2,6,22,86,338,1318,5106,19718,76066,293398,1131794,4366374,

%T 16846018,64995254,250765298,967503814,3732821922,14401956182,

%U 55565542354,214382633062,827129764994,3191227078902,12312373271986,47503525349126,183277819294562

%N Number of permutations of length n which avoid the patterns 1342, 4213.

%H Colin Barker, <a href="/A116707/b116707.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,16,-4).

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

%F a(n) = 7*a(n-1) - 16*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>3. - _Colin Barker_, Oct 20 2017

%t CoefficientList[Series[-(x - 1)*(2*x - 1)^2/(4*x^4 - 16*x^3 + 16*x^2 - 7*x + 1), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 04 2022 *)

%o (PARI) Vec(x*(1 - x)*(1 - 2*x)^2 / (1 - 7*x + 16*x^2 - 16*x^3 + 4*x^4) + O(x^40)) \\ _Colin Barker_, Oct 20 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006