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Number of permutations of length n which avoid the patterns 231, 51234.
1

%I #13 Nov 01 2017 18:27:05

%S 1,2,5,14,41,119,336,927,2527,6870,18717,51155,140120,384147,1053147,

%T 2886182,7906953,21657679,59318944,162475127,445041287,1219069014,

%U 3339354501,9147387195,25057021032,68637206987,188013260835,515011570790,1410735630289

%N Number of permutations of length n which avoid the patterns 231, 51234.

%H Colin Barker, <a href="/A116848/b116848.txt">Table of n, a(n) for n = 1..1000</a>

%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,-14,17,-10,4).

%F G.f.: x*(1 - 4*x + 7*x^2 - 5*x^3 + 3*x^4) / (1 - 6*x + 14*x^2 - 17*x^3 + 10*x^4 - 4*x^5).

%F a(n) = 6*a(n-1) - 14*a(n-2) + 17*a(n-3) - 10*a(n-4) + 4*a(n-5) for n>5. - _Colin Barker_, Nov 01 2017

%o (PARI) Vec(x*(1 - 4*x + 7*x^2 - 5*x^3 + 3*x^4) / (1 - 6*x + 14*x^2 - 17*x^3 + 10*x^4 - 4*x^5) + O(x^40)) \\ _Colin Barker_, Nov 01 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006