A294801 - OEIS

%I #12 Mar 21 2021 21:22:45

%S 1,1,2,6,21,73,239,736,2158,6102,16813,45493,121567,322108,848654,

%T 2227722,5834253,15258361,39874967,104169568,272109046,710846406,

%U 1857283957,4853664901,12686932951,33169384588,86737334054,226858067466,593434214373,1552572159577,4062403215263,10630610953408

%N Number of permutations of [n] avoiding {4231, 1324, 2341}.

%H Colin Barker, <a href="/A294801/b294801.txt">Table of n, a(n) for n = 0..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 1 No 84.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-41,89,-110,77,-28,4).

%F From _Colin Barker_, Apr 25 2020: (Start)

%F G.f.: (1 - 9*x + 33*x^2 - 62*x^3 + 64*x^4 - 36*x^5 + 7*x^6) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x + x^2)).

%F a(n) = 10*a(n-1) - 41*a(n-2) + 89*a(n-3) - 110*a(n-4) + 77*a(n-5) - 28*a(n-6) + 4*a(n-7) for n>6.

%F (End)

%p (1 -9*x +33*x^2 -62*x^3 +64*x^4 -36*x^5 +7*x^6)/((1 -3*x +x^2)*(1 -2*x)^2*(1 -x)^3) ;

%p taylor(%,x=0,40) ;

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 9*x + 33*x^2 - 62*x^3 + 64*x^4 - 36*x^5 + 7*x^6) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^40)) \\ _Colin Barker_, Apr 25 2020

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 09 2017