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Number of permutations of length n which avoid the patterns 231, 3214, 4312.
1

%I #17 Nov 29 2018 10:35:12

%S 1,2,5,12,27,59,126,265,551,1136,2327,4743,9630,19493,39363,79336,

%T 159659,320915,644414,1293009,2592783,5196512,10410735,20850127,

%U 41746622,83568269,167257931,334712280,669742371,1339998971

%N Number of permutations of length n which avoid the patterns 231, 3214, 4312.

%H Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p22">Non-contiguous pattern avoidance in binary trees</a>. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227. - From _N. J. A. Sloane_, Feb 01 2013

%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,-1,-2).

%F G.f.: A(x) = (x^3-x+1)*x/((2*x-1)*(x^2+x-1)).

%F a(n) = A257113(n+1) - A000045(n+2). - _R. J. Mathar_, Nov 07 2017

%t CoefficientList[Series[(x^3-x+1)/((2*x-1)*(x^2+x-1)), {x, 0, 50}], x] (* _Stefano Spezia_, Nov 29 2018 *)

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006