A294698 - OEIS

%I #20 Mar 21 2021 21:16:51

%S 1,1,2,6,21,74,248,780,2309,6483,17407,45028,112921,275964,660030,

%T 1550320,3586449,8190493,18500893,41399992,91896773,202564062,

%U 443789172,967093220,2097536909,4530328551,9748157339,20905142940,44695397953,95295673696,202670082154

%N Number of permutations of [n] avoiding {1423, 1234, 3412}.

%H Colin Barker, <a href="/A294698/b294698.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1708.00832">Enumeration of small Wilf Classes avoiding 1342 and two other 4-letter patterns</a>, arXiv:1708.00832  [math.CO] (2017). Table 1 No 118.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (13,-75,253,-553,819,-833,575,-258,68,-8).

%F G.f.: (1 - 12*x + 64*x^2 - 198*x^3 + 393*x^4 - 521*x^5 + 463*x^6 - 269*x^7 + 95*x^8 - 17*x^9) / ((1 - x)^7*(1 - 2*x)^3).

%F From _Colin Barker_, Nov 07 2017: (Start)

%F a(n) = (1/720)*(720*(41 - 5*2^(3+n)) + 6*(2812 + 465*2^n)*n + 2*(2627 + 45*2^n)*n^2 + 765*n^3 + 145*n^4 + 3*n^5 + n^6).

%F a(n) = 13*a(n-1) - 75*a(n-2) + 253*a(n-3) - 553*a(n-4) + 819*a(n-5) - 833*a(n-6) + 575*a(n-7) - 258*a(n-8) + 68*a(n-9) - 8*a(n-10) for n > 9. (End)

%p p := 1-12*x+64*x^2-198*x^3+393*x^4-521*x^5+463*x^6-269*x^7+95*x^8-17*x^9 ;

%p q := (1-x)^7*(1-2*x)^3 ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 12*x + 64*x^2 - 198*x^3 + 393*x^4 - 521*x^5 + 463*x^6 - 269*x^7 + 95*x^8 - 17*x^9) / ((1 - x)^7*(1 - 2*x)^3) + O(x^40)) \\ _Colin Barker_, Nov 07 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 07 2017