

A274258


Factorfree 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
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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 (3n,5n) that stay below the line y=5/3x and also do not contain a proper subpath 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 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) = 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 subpath of small size, i.e. ENEEEENNNNENNNNN is a factorfree Dyck word but ENEENNENNNEENNNN contains the factor EENNENNN.


CROSSREFS

A005807 enumerates factorfree Dyck words with slope 3/2. A274052 enumerates factorfree Dyck words with slope 5/2. A274244 enumerates factorfree Dyck words with slope 7/2. A274256 enumerates factorfree Dyck words with slope 9/2. A274257 enumerates factorfree 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



