A116809 - OEIS

A116809

Number of permutations of length n which avoid the patterns 1432, 2134, 2143.

%I #17 Sep 19 2018 04:20:15

%S 1,2,6,21,76,273,971,3439,12172,43098,152649,540730,1915445,6785029,

%T 24034177,85134498,301565746,1068215101,3783864272,13403320805,

%U 47477655647,168176809999,595721056436,2110181402286,7474749309041

%N Number of permutations of length n which avoid the patterns 1432, 2134, 2143.

%H Robert Israel, <a href="/A116809/b116809.txt">Table of n, a(n) for n = 1..1810</a>

%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 [math.CO] (2017), Table 2 No 189.

%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 (6,-12,13,-5,1).

%F G.f.: A(x) = -{(x-1)^4x}/{x^5-5x^4+13x^3-12x^2+6x-1}

%p f:= gfun:-rectoproc({a(n)-5*a(n+1)+13*a(n+2)-12*a(n+3)+6*a(n+4)-a(n+5), a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 6, a(4) = 21, a(5) = 76},a(n),remember):

%p map(f, [$1..30]); # _Robert Israel_, Jun 02 2016

%t LinearRecurrence[{6, -12, 13, -5, 1}, {1, 2, 6, 21, 76}, 25] (* _Jean-François Alcover_, Sep 19 2018 *)

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006