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A274259 Factor-free Dyck words with slope 7/3 and length 10n 0
1, 12, 570, 44689, 4223479, 441010458, 49014411306, 5685822210429, 680500195656621, 83406972284096638, 10416465145620729162, 1320749077779826216029, 169570747575202480367168, 22000830732097549119672094, 2880094468241888675318895339, 379941591968957300338548388051, 50458777676743899501139029335858 (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,7n) that stay below the line y=7/3x and also do not contain a proper sub-path of smaller size.

LINKS

Table of n, a(n) for n=0..16.

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) = 570 since there are 570 lattice paths (allowing only north and east steps) starting at (0,0) and ending at (6,14) that stay below the line y=7/3x and also do not contain a proper sub-path of small size, i.e. ENNENENNNENNENNNENNN is a factor-free Dyck word but ENNENNENNEENNNNNENNN contains the factor ENNEENNNNN.

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. A274257 enumerates factor-free Dyck words with slope 4/3.  A274258 enumerates factor-free Dyck words with slope 5/3.

Sequence in context: A133415 A192602 A227143 * A192603 A192604 A192605

Adjacent sequences:  A274256 A274257 A274258 * A274260 A274261 A274262

KEYWORD

nonn

AUTHOR

Michael D. Weiner, Jun 16 2016

STATUS

approved

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)