Schröder number

GPTKB entity

Statements (23)
Predicate Object
gptkbp:instanceOf integer sequence
gptkbp:alsoKnownAs gptkb:large_Schröder_number
gptkbp:first_terms 2
1
1806
22
6
90
394
206098
41586
8558
gptkbp:generatingFunction (1-x-sqrt(1-6x+x^2))/(2x)
https://www.w3.org/2000/01/rdf-schema#label Schröder number
gptkbp:namedAfter gptkb:Ernst_Schröder
gptkbp:numberOfRooms number of lattice paths from (0,0) to (n,n) with steps (1,0), (0,1), (1,1) that do not rise above the line y=x
gptkbp:OEIS gptkb:A006318
gptkbp:recurrence S(n) = S(n-1) + sum_{k=1}^{n-1} S(k) * S(n-k) for n > 0, S(0) = 1
gptkbp:relatedTo gptkb:Catalan_number
gptkb:little_Schröder_number
gptkbp:usedIn combinatorics
gptkbp:bfsParent gptkb:large_Schröder_number
gptkbp:bfsLayer 8