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Number of permutations of [n] avoiding {3412, 4132, 1324}.
1

%I #19 Mar 21 2021 21:55:54

%S 1,1,2,6,21,73,239,740,2194,6298,17653,48621,132199,356040,952154,

%T 2533014,6712221,17734489,46753127,123048884,323441770,849373210,

%U 2228871757,5845630221,15324795631,40162310568,105229244354,275659639590,722018109189,1890931558153,4951850306303

%N Number of permutations of [n] avoiding {3412, 4132, 1324}.

%H Colin Barker, <a href="/A294694/b294694.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1708.00832">Enumeration of small Wilf Classes avoiding 1342 and two other 4-letter patterns</a>, arXiv:1708.00832 [math.CO] (2017). Table 1 No 86.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25,39,-32,13,-2).

%F O.g.f.: (1 - 7*x + 19*x^2 - 24*x^3 + 16*x^4 - 4*x^5 - x^6 + 2*x^7)/((1 - 2*x)*(1 - 3*x + x^2)*(1 - x)^3).

%F a(n) = 8*a(n-1) - 25*a(n-2) + 39*a(n-3) - 32*a(n-4) + 13*a(n-5) - 2*a(n-6) for n>7. - _Colin Barker_, Nov 07 2017

%p p := 1-7*x+19*x^2-24*x^3+16*x^4-4*x^5-x^6+2*x^7 ;

%p q := (1-x)^3*(1-2*x)*(1-3*x+x^2) ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 7*x + 19*x^2 - 24*x^3 + 16*x^4 - 4*x^5 - x^6 + 2*x^7) / ((1 - x)^3*(1 - 2*x)*(1 - 3*x + x^2)) + O(x^30)) \\ _Colin Barker_, Nov 07 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 07 2017