A116804 - OEIS

%I #12 Nov 08 2017 04:31:57

%S 1,2,6,21,70,200,481,1004,1886,3270,5325,8246,12254,17596,24545,33400,

%T 44486,58154,74781,94770,118550,146576,179329,217316,261070,311150,

%U 368141,432654,505326,586820

%N Number of permutations of length n which avoid the patterns 1234, 1432, 4231.

%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 (2017), Table 2 No 11.

%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)

%F G.f.: A(x) = -{x(5x^8-2x^7-x^6+9x^5+10x^4+x^3+6x^2-3x+1)}/{(x-1)^5}

%F For n >= 5, a(n) = (13n^4 - 156n^3 + 893n^2 - 2790n + 3840)/12. - Franklin T. Adams-Watters, Sep 16 2006

%p cn := [1,-4,7,-4,6,9,9,-1,-2,5] ;

%p p := add(cn[i]*x^(i-1),i=1..nops(cn)) ;

%p q := (1-x)^5 ;

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

%p gfun[seriestolist](%) ; # _R. J. Mathar_, Nov 07 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006