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%I #13 May 06 2017 09:30:39
%S 1,2,5,12,25,44,69,100,137,180,229,284,345,412,485,564,649,740,837,
%T 940,1049,1164,1285,1412,1545,1684,1829,1980,2137,2300,2469,2644,2825,
%U 3012,3205,3404,3609,3820,4037,4260,4489,4724,4965,5212,5465,5724,5989,6260
%N Number of permutations of length n which avoid the patterns 213, 1234, 4312.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: A(x) = -{x(2x^4+2x^3+2x^2-x+1)}/{(x-1)^3}
%F For n >= 3, a(n) = 3n^2 - 14n + 20. - _Franklin T. Adams-Watters_, Sep 16 2006
%p A116720 := proc(n) coeftayl(-x*(2*x^4+2*x^3+2*x^2-x+1)/(x-1)^3,x=0,n) ; end: seq(A116720(n),n=1..60) ; # _R. J. Mathar_, Jan 23 2008
%t f[n_]:=n+(n+1)*(n+2)+(n+3)*(n+4)+(n+5)*(n+6); lst={1,2};Do[AppendTo[lst,f[n]],{n,-3,5!}];lst [_Vladimir Joseph Stephan Orlovsky_, Oct 08 2009]
%t LinearRecurrence[{3,-3,1},{1,2,5,12,25},50] (* _Harvey P. Dale_, May 06 2017 *)
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
%E More terms from _R. J. Mathar_, Jan 23 2008
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