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A116728 Number of permutations of length n which avoid the patterns 321, 1243, 2134.

%I A116728 #20 Oct 11 2022 00:35:27
%S A116728 1,2,5,12,19,26,33,40,47,54,61,68,75,82,89,96,103,110,117,124,131,138,
%T A116728 145,152,159,166,173,180,187,194,201,208,215,222,229,236,243,250,257,
%U A116728 264,271,278,285,292,299,306,313,320,327,334,341,348,355,362,369
%N A116728 Number of permutations of length n which avoid the patterns 321, 1243, 2134.
%H A116728 Nathaniel Johnston, <a href="/A116728/b116728.txt">Table of n, a(n) for n = 1..5000</a>
%H A116728 Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H A116728 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A116728 G.f.: x*(1 + 2*x^2 + 4*x^3) / (1 - x)^2.
%F A116728 For n >= 3, a(n) = 7*n - 16. - _Franklin T. Adams-Watters_, Sep 16 2006
%F A116728 a(n) = 2*a(n-1) - a(n-2) for n=4. - _Colin Barker_, Oct 24 2017
%F A116728 a(n) = A017041(n-3) for n > 2. - _Georg Fischer_, Oct 07 2018
%F A116728 E.g.f.: exp(x)*(7*x - 16) + 2*(x^2 + 5*x + 8). - _Stefano Spezia_, Oct 10 2022
%p A116728 t := taylor((4*x^3+2*x^2+1)*x/(x-1)^2,x,51):seq(coeff(t,x,n),n=1..50); # _Nathaniel Johnston_, Apr 27 2011
%o A116728 (PARI) Vec(x*(1 + 2*x^2 + 4*x^3) / (1 - x)^2 + O(x^70)) \\ _Colin Barker_, Oct 24 2017
%Y A116728 Cf. A017041.
%K A116728 nonn,easy
%O A116728 1,2
%A A116728 _Lara Pudwell_, Feb 26 2006