A294804 - OEIS

%I #15 Nov 05 2025 15:22:41

%S 1,1,2,6,21,73,242,762,2290,6610,18434,49922,131842,340738,864258,

%T 2156546,5304322,12881922,30932994,73531394,173211650,404684802,

%U 938475522,2161639426,4948230146,11262754818,25501368322,57461964802,128899350530,287947358210,640755433474,1420694650882,3139352657922,6915165782018

%N Number of permutations of [n] avoiding {1324, 3142, 4231}.

%H Colin Barker, <a href="/A294804/b294804.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Callan and T. Mansour, <a href="https://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 99.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-32,56,-48,16).

%F G.f.: (1 - 8*x + 25*x^2 - 36*x^3 + 23*x^4 - 4*x^5 + x^6) / ((1 - x)*(1 - 2*x)^4).

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

%F a(n) = (1/192)*(384 - 51*2^(2+n) + 17*2^(3+n)*n - 27*2^n*n^2 + 5*2^n*n^3) for n>1.

%F a(n) = 9*a(n-1) - 32*a(n-2) + 56*a(n-3) - 48*a(n-4) + 16*a(n-5) for n>6.

%F (End)

%p (1 -8*x +25*x^2 -36*x^3 +23*x^4 -4*x^5 +x^6)/((1 -x)*(1 -2*x)^4) ;

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

%p gfun[seriestolist](%) ;

%t LinearRecurrence[{9,-32,56,-48,16},{1,1,2,6,21,73,242},40] (* _Harvey P. Dale_, Jul 22 2020 *)

%o (PARI) Vec((1 - 8*x + 25*x^2 - 36*x^3 + 23*x^4 - 4*x^5 + x^6) / ((1 - x)*(1 - 2*x)^4) + O(x^30)) \\ _Colin Barker_, Nov 09 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 09 2017