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Number of bi-secondary structures of size N.
0

%I #4 Feb 27 2009 03:00:00

%S 1,1,1,2,5,13,37,112,365,1253,4542,17149,67455,274134,1150125

%N Number of bi-secondary structures of size N.

%C A BiSecondary Structure(BSS) is a RNA graph that can be drawn without crossings using at most two halfplanes. The numbers displayed here were obtained by first generating all secondary structures of a given size and then by carefully counting possible completions on the second halfplane. Keep in mind that the simple shuffling of two secondary structures would yield many isomorphic RNA graphs.

%e Encoding the secondary structure on the first halfplane with '()', on the 2nd with '[]' and unpaired bases with '-'. For n=4, bss(n)=5:

%e .... (.). (..) .(.) ([)]

%e Notice that '[(])' must not be counted, as it is isomorphic to '([)]'.

%Y Cf. A004148.

%K easy,nonn

%O 0,4

%A Yann Ponty (Yann.Ponty(AT)lri.fr), May 25 2006