

A274244


Factorfree 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
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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 subpath 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 factorfree Dyck words, arXiv:1606.02183 [math.CO], 2016.
P. Duchon, On the enumeration and generation of generalized Dyck words, Discrete Mathematics, 225 (2000), 121135.


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 subpath of small size, i.e. EEENNNNENNNNNNNNNN is a factorfree Dyck word but EEENNENNNNNNNNNNNN contains the factor ENNENNNNN.


CROSSREFS

A005807 enumerates factorfree Dyck words with slope 3/2. A274052 enumerates factorfree 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



