A116838 - OEIS

%I #12 Dec 28 2023 21:49:02

%S 1,2,6,21,72,233,719,2146,6260,17968,50967,143278,399960,1110203,

%T 3067479,8442903,23163006,63371999,172967309,471115792,1280844662,

%U 3476636122,9423007521,25506378316,68958653982,186231636833

%N Number of permutations of length n which avoid the patterns 1342, 3421, 4312.

%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 53.

%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_09">Index entries for linear recurrences with constant coefficients</a>, signature (13,-72,222,-418,496,-369,165,-40,4).

%F G.f.: x*(x^9 -8x^8 +34x^7 -97x^6 +183x^5 -205x^4 +135x^3 -52x^2 +11x -1)/((x^2-3x+1)^2 (2x-1)^2 (x-1)^3).

%t CoefficientList[Series[(x^9 - 8 x^8 + 34 x^7 - 97 x^6 + 183 x^5 - 205 x^4 + 135 x^3 - 52 x^2 + 11 x - 1)/((x^2 - 3 x + 1)^2 (2 x - 1)^2 (x - 1)^3), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Dec 28 2023 *)

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006