A143657 Number of 4-noncrossing stack-free partial matching without 1-arcs.

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

Offset: 1

Author

Jonathan Vos Post, Aug 28 2008

Keywords

• nonn
• more

Comments

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.

Links

• Emma Y. Jin and Christian M. Reidys, RNA-LEGO: Combinatorial Design of Pseudoknot RNA, arXiv:0711.1405 [q-bio.BM], 2007.

Crossrefs

Cf. A132441.

Formula

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.

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