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A274258 Factor-free Dyck words with slope 5/3 and length 8n 1
1, 7, 133, 4140, 154938, 6398717, 281086555, 12882897819, 609038885805, 29481041746958, 1453894927584477, 72789271870852237, 3689808842747726368, 189006099916444293090, 9768094831949586349262, 508712466332195692590121, 26670630123516854616641671, 1406503552584980596900001922, 74559627811441047591493767590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of lattice paths (allowing only north and east steps) starting at (0,0) and ending at (3n,5n) that stay below the line y=5/3x and also do not contain a proper sub-path of smaller size.

LINKS

Table of n, a(n) for n=0..18.

Daniel Birmajer, Juan B. Gil, Michael D. Weiner, On rational Dyck paths and the enumeration of factor-free Dyck words, arXiv:1606.02183 [math.CO], 2016.

P. Duchon, On the enumeration and generation of generalized Dyck words, Discrete Mathematics, 225 (2000), 121-135.

EXAMPLE

a(2) = 133 since there are 133 lattice paths (allowing only north and east steps) starting at (0,0) and ending at (6,10) that stay below the line y=5/3x and also do not contain a proper sub-path of small size, i.e. ENEEEENNNNENNNNN is a factor-free Dyck word but ENEENNENNNEENNNN contains the factor EENNENNN.

CROSSREFS

A005807 enumerates factor-free Dyck words with slope 3/2.  A274052 enumerates factor-free Dyck words with slope 5/2.  A274244 enumerates factor-free Dyck words with slope 7/2. A274256 enumerates factor-free Dyck words with slope 9/2. A274257 enumerates factor-free Dyck words with slope 4/3.

Sequence in context: A110111 A245318 A274788 * A251577 A082164 A229464

Adjacent sequences:  A274255 A274256 A274257 * A274259 A274260 A274261

KEYWORD

nonn

AUTHOR

Michael D. Weiner, Jun 16 2016

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)