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 A116711 Number of permutations of length n which avoid the patterns 123, 3214, 4312. 3

%I #12 Oct 23 2017 19:56:31

%S 1,2,5,12,23,36,51,68,87,108,131,156,183,212,243,276,311,348,387,428,

%T 471,516,563,612,663,716,771,828,887,948,1011,1076,1143,1212,1283,

%U 1356,1431,1508,1587,1668,1751,1836,1923,2012,2103,2196,2291,2388,2487,2588

%N Number of permutations of length n which avoid the patterns 123, 3214, 4312.

%H Colin Barker, <a href="/A116711/b116711.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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3.

%F For n >= 4, a(n) = n^2 + 2*n - 12. - _Franklin T. Adams-Watters_, Sep 16 2006

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. - _Colin Barker_, Oct 23 2017

%o (PARI) Vec(x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3 + O(x^50)) \\ _Colin Barker_, Oct 23 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)