[seqfan] Dyck paths with descents restricted by ascents

David Scambler dscambler at bmm.com
Sun Jan 9 02:35:07 CET 2011


Proposed A179544,

Dyck paths of semi-length n for which the set of ascent lengths and the 
set of descent lengths are the same partition of n.

1, 1, 2, 5, 12, 30, 80, 219, 614, 1766, 5206, 15646, 47834, 148602, 468110, ...

e.g.

For n=4 the paths UUUDDUDD and UUDUUDDD fail the definition because {2,2} != {3,1} 
so a(4) = 12 rather than equal to Catalan(4)=14

cheers 
dave



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