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%I #23 Apr 03 2022 13:49:59
%S 1,1,2,6,23,94,391,1633,6827,28548,119384,499255,2087854,8731285,
%T 36513737,152698377,638575958,2670488470,11167831459,46703238346,
%U 195310296371,816776592369,3415713427499,14284320005992,59736216859096,249813474014875,1044705792912602
%N Permutations in S_n avoiding the patterns {4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, 45231}.
%C A(n) is also the number of w in S_n for which the number of repeated letters in a reduced decomposition of w equals the number of 321- and 3412-patterns in w.
%C The generating function can be automatically computed by the Maple package INSENC listed in the links. - _Vincent Vatter_, Jun 16 2011
%H Harvey P. Dale, <a href="/A191721/b191721.txt">Table of n, a(n) for n = 0..1000</a>
%H B. E. Tenner, <a href="http://arxiv.org/abs/1106.2839">Repetition in reduced decompositions</a>, arXiv:1106.2839 [math.CO]
%H V. Vatter, <a href="http://www.math.ufl.edu/~vatter/programs/insenc/">Maple package INSENC</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3,-2,1).
%F G.f.: (1-4*x+x^3)/((1-x)*(1-4*x-x^2+x^3)). - _Vincent Vatter_, Jun 16 2011
%e A(4)=23 because all permutations in S_4 except 4321 avoid these patterns. Also, all permutations in S_4 except 4321 have repeated letters equaling the number of 321- and 3412-patterns. (Note that 4321 has 3 repeated letters, but 4 of these patterns.)
%t LinearRecurrence[{5,-3,-2,1},{1,1,2,6},30] (* _Harvey P. Dale_, Apr 03 2022 *)
%K nonn
%O 0,3
%A _Bridget Tenner_, Jun 13 2011
%E a(0)=1 prepended and more terms from _Alois P. Heinz_, Jun 17 2021
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