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Number of 4-noncrossing stack-free partial matching without 1-arcs.
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%I #7 Jan 13 2024 10:44:46

%S 1,1,2,5,12,32,95,301,1001,3495,12708,47932,186581,747619,3073207

%N Number of 4-noncrossing stack-free partial matching without 1-arcs.

%C This sequence is the second row of Jin and Reidys table, p. 15; the first row, number of 3-noncrossing stack-free partial matching without 1-arcs, is A132441.

%H Emma Y. Jin and Christian M. Reidys, <a href="http://arxiv.org/abs/0711.1405">RNA-LEGO: Combinatorial Design of Pseudoknot RNA</a>, arXiv:0711.1405 [q-bio.BM], 2007.

%F a(n) = C_4(n,h) = SUM[b=0..{h-1}](-1)^{h-b-1}{h-1 Choose b}{T}_4(h-2h+2b+2,b+1); where the T function is defined in Jin and Reidys.

%F Asymptotically a(n) ~ (1.217 * 10^7)*(n^(-21/2))*(3.0382^n).

%Y Cf. A132441.

%K nonn,more

%O 1,3

%A _Jonathan Vos Post_, Aug 28 2008