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%I #14 Jul 08 2020 20:40:52
%S 1,1,3,11,41,151,553,2023,7401
%N Number of hare pop-stack sortable Cayley permutations.
%C Also, the set of Cayley permutations avoiding 231, 312, and 2121.
%H Giulio Cerbai, <a href="https://arxiv.org/abs/2003.02536">Sorting Cayley permutations with pattern-avoiding machines</a>, arXiv:2003.02536 [math.CO], 2020. See p. 16.
%F Conjectures from _Colin Barker_, Jun 24 2020: (Start)
%F G.f.: (1 - 4*x + 4*x^2 - 2*x^3) / (1 - 5*x + 6*x^2 - 4*x^3).
%F a(n) = 5*a(n-1) - 6*a(n-2) + 4*a(n-3) for n>3.
%F (End)
%Y Cf. A000670, A226316.
%K nonn,more
%O 0,3
%A _Michael De Vlieger_, Jun 23 2020
%E a(7)-a(8) from Giulio Cerbai via _Michael De Vlieger_, Jun 24 2020
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