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Number of permutations of length n which avoid the patterns 1234, 4312.
0

%I #13 Jul 07 2017 07:04:56

%S 1,2,6,22,86,321,1085,3266,8797,21478,48206,100728,198046,369617,

%T 659505,1131656,1876481,3018946,4728382,7230242,10820046,15879769,

%U 22896941,32486742,45417389,62639126,85317142,114868756,153005222,201778521

%N Number of permutations of length n which avoid the patterns 1234, 4312.

%D Kremer, Darla; and Shiu, Wai Chee; Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268 (2003), no. 1-3, 171-183. MR1983276 (2004b:05006). See Table 1.

%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Enumerations_of_specific_permutation_classes#Classes_avoiding_two_patterns_of_length_4">Permutation classes avoiding two patterns of length 4</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F G.f.: x*(4*x^8-19*x^7+32*x^6-39*x^5+62*x^4-44*x^3+24*x^2-7*x+1)/(1-x)^9

%F a(n) = (21*n^8 - 48*n^7 - 966*n^6 + 7728*n^5 - 8211*n^4 - 72912*n^3 + 311556*n^2 - 418608*n + 241920)/60480. - Franklin T. Adams-Watters, Sep 16 2006

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006