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Number of permutations of [n] avoiding {1324, 2431, 3142}.
0

%I #8 Mar 21 2021 21:38:27

%S 1,1,2,6,21,76,275,989,3539,12631,45066,161021,576887,2074166,7488003,

%T 27150233,98878251,361680595,1328574654,4900021037,18141052047,

%U 67402330234,251263851255,939561899651,3523414637736,13248113693491,49935804727105,188651583360524,714214447347319

%N Number of permutations of [n] avoiding {1324, 2431, 3142}.

%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 193.

%F D-finite with recurrence 2*(n+1)*a(n) +(-19*n+3)*a(n-1) +2*(31*n-39)*a(n-2) +2*(-40*n+93)*a(n-3) +(33*n-107)*a(n-4) +2*(-2*n+9)*a(n-5)=0. - _R. J. Mathar_, Jan 18 2021

%p C := (1-sqrt(1-4*x))/2/x ;

%p (x -1 +(x^2 -5*x +2)*C)/(1 -3*x +x^2) ;

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

%p gfun[seriestolist](%) ;

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 09 2017