A294800 - OEIS

%I #12 Nov 05 2025 15:22:41

%S 1,1,2,6,21,73,238,726,2101,5857,15926,42626,112997,297861,782666,

%T 2052958,5379953,14091781,36901646,96621062,252971401,662305301,

%U 1733959342,4539590666,11884834161,31114937393,81460008218,213265122686,558335401141,1461741128617,3826888039926,10018923054526,26229881196037

%N Number of permutations of [n] avoiding {1324, 2341, 3421}.

%H Colin Barker, <a href="/A294800/b294800.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Callan, 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 80.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,45,-45,26,-8,1).

%F G.f.: (1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)).

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

%F a(n) = (1/60)*(-3*2^(2-n)*(15*2^n + 2*(-5+sqrt(5))*(3+sqrt(5))^n - 2*(3-sqrt(5))^n*(5+sqrt(5))) + 80*n - 85*n^2 + 10*n^3 - 5*n^4).

%F a(n) = 8*a(n-1) - 26*a(n-2) + 45*a(n-3) - 45*a(n-4) + 26*a(n-5) - 8*a(n-6) + a(n-7) for n>6.

%F (End)

%p (1 -7*x +20*x^2 -29*x^3 +25*x^4 -10*x^5 +2*x^6)/((1 -x)^5*(1 -3*x +x^2)) ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)) + O(x^30)) \\ _Colin Barker_, Nov 09 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 09 2017