A294772 - OEIS

%I #11 Mar 21 2021 21:21:41

%S 1,1,2,6,21,76,270,930,3114,10196,32820,104283,328048,1023854,3175395,

%T 9797833,30104416,92174093,281393563,856933273,2604185761,7899961881,

%U 23928712717,72385213846,218724040451,660278241111,1991584682200,6002897801720,18082374709679

%N Number of permutations of [n] avoiding {4132, 4123, 1243}.

%H Colin Barker, <a href="/A294772/b294772.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 2 No 186.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,83,-97,64,-22,3).

%F G.f.: (1 - 9*x + 32*x^2 - 57*x^3 + 55*x^4 - 27*x^5 + 4*x^6) / ((1 - x)^4*(1 - 3*x)*(1 - 3*x + x^2)).

%F From _Colin Barker_, Nov 09 2017: (Start)

%F a(n) = (35/16 + (13*3^n)/16 - ((3-sqrt(5))/2)^n - ((3+sqrt(5))/2)^n - (7*n)/6 + (5*n^2)/8 - n^3/12).

%F a(n) = 10*a(n-1) - 40*a(n-2) + 83*a(n-3) - 97*a(n-4) + 64*a(n-5) - 22*a(n-6) + 3*a(n-7) for n>6.

%F (End)

%p -(-27*x^5+55*x^4-57*x^3+32*x^2-9*x+1+4*x^6)/((3*x-1)*(x^2-3*x+1)*(x-1)^4) ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 9*x + 32*x^2 - 57*x^3 + 55*x^4 - 27*x^5 + 4*x^6) / ((1 - x)^4*(1 - 3*x)*(1 - 3*x + x^2)) + O(x^30)) \\ _Colin Barker_, Nov 09 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017