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A274244 Factor-free Dyck words with slope 7/2 and length 9n. 5
1, 4, 34, 494, 8615, 165550, 3380923, 71999763, 1580990725, 35537491360, 813691565184, 18911247654404, 444978958424224, 10579389908116344, 253756528273411250, 6133110915783398175, 149219383150626519874, 3651756292682801022384, 89830021324956206790496, 2219945238901447637080235, 55088272581138888326634644 (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 (2n,7n) that stay below the line y=7/2x and also do not contain a proper sub-path of smaller size.

LINKS

Table of n, a(n) for n=0..20.

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) = 34 since there are 34 lattice paths (allowing only north and east steps) starting at (0,0) and ending at (4,14) that stay below the line y=7/2x and also do not contain a proper sub-path of small size, i.e. EEENNNNENNNNNNNNNN is a factor-free Dyck word but EEENNENNNNNNNNNNNN contains the factor ENNENNNNN.

CROSSREFS

A005807 enumerates factor-free Dyck words with slope 3/2. A274052 enumerates factor-free Dyck words with slope 5/2.

Sequence in context: A156325 A248654 A111169 * A002105 A198717 A198908

Adjacent sequences:  A274241 A274242 A274243 * A274245 A274246 A274247

KEYWORD

nonn

AUTHOR

Michael D. Weiner, Jun 15 2016

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)