Schröder Number
The Schröder number 
is the number of Lattice Paths in the Cartesian plane that start at(0, 0), end at 
, contain no points above the line 
, and are composed only of steps (0, 1), (1, 0), and (1,1), i.e., 
, 
, and 
. The diagrams illustrating the paths generating 
, 
, and 
are illustrated above. The numbers are given by the Recurrence Relation
where
, and the first few are 2, 6, 22, 90, ... (Sloane's A006318). The Schröder Numbers bear the same relation tothe Delannoy Numbers as the Catalan Numbers do to the BinomialCoefficients.See also Binomial Coefficient, Catalan Number, Delannoy Number, Lattice Path, Motzkin Number,p-Good Path
References
Sloane, N. J. A. SequenceA006318/M1659in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Nyquist Sampling
- Néron-Severi Group
- Nöther
- Obelus
- Object
- Oblateness
- Oblate Spheroid
- Oblate Spheroidal Coordinates
- Oblate Spheroidal Wave Function
- Oblate Spheroid Geodesic
- Oblique Angle
- Oblong Number
- Obstruction
- Obtuse Angle
- Obtuse Triangle
- Ochoa Curve
- Octacontagon
- Octadecagon
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- Octagonal Number
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- Octahedron