A294771 - OEIS

%I #14 Mar 21 2021 21:21:27

%S 1,1,2,6,21,75,259,862,2808,9090,29489,96076,314011,1027749,3364559,

%T 11012071,36033146,117891838,385711145,1261999184,4129291969,

%U 13511534900,44211907218,144668866862,473380823897,1548980397627,5068520414694,16585048409912,54269098388346,177577820365484

%N Number of permutations of [n] avoiding {4231, 2341, 4123}.

%H Colin Barker, <a href="/A294771/b294771.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 152.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (10,-42,99,-144,134,-83,31,-5).

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

%F G.f.: (1 - x)^6*(1 - 3*x + x^2) / (1 - 10*x + 42*x^2 - 99*x^3 + 144*x^4 - 134*x^5 + 83*x^6 - 31*x^7 + 5*x^8).

%F a(n) = 10*a(n-1) - 42*a(n-2) + 99*a(n-3) - 144*a(n-4) + 134*a(n-5) - 83*a(n-6) +  31*a(n-7) - 5*a(n-8) for n>8.

%F (End)

%p (x-1)^6*(x^2-3*x+1)/(5*x^8-31*x^7+83*x^6-134*x^5+144*x^4-99*x^3+42*x^2-10*x+1) ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - x)^6*(1 - 3*x + x^2) / (1 - 10*x + 42*x^2 - 99*x^3 + 144*x^4 - 134*x^5 + 83*x^6 - 31*x^7 + 5*x^8) + O(x^30)) \\ _Colin Barker_, Apr 25 2020

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017