Identifier
-
Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
St000932: Dyck paths ⟶ ℤ (values match St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra., St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless.)
Values
=>
Cc0005;cc-rep-0
Cc0005;cc-rep
[1,0]=>[1,1,0,0]=>0
[1,0,1,0]=>[1,1,0,1,0,0]=>1
[1,1,0,0]=>[1,1,1,0,0,0]=>0
[1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>0
[1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>0
[1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>0
[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
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Description
The number of occurrences of the pattern UDU in a Dyck path.
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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