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 A274244 Number of factor-free Dyck words with slope 7/2 and length 9n. 7
 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. FORMULA Conjectural o.g.f.: Let E(x) = exp( Sum_{n >= 1} binomial(9*n, 2*n)*x^n/n ). Then A(x) = ( x/series reversion of x*E(x) )^(1/9) = 1 + 4*x + 34*x^2 + 494*x^3 + .... Equivalently, [x^n]( A(x)^(9*n) ) = binomial(9*n, 2*n) for n = 0,1,2,.... - Peter Bala, Jan 01 2020 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; e.g., EEENNNNENNNNNNNNNN is a factor-free Dyck word but EEENNENNNNNNNNNNNN contains the factor ENNENNNNN. CROSSREFS Factor-free Dyck words: A005807 (slope 3/2), A274052 (slope 5/2), A274256 (slope 9/2), A274257 (slope 4/3), A274259 (slope 7/3). Cf. A060941. Sequence in context: A248654 A336495 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 June 2 22:56 EDT 2023. Contains 363102 sequences. (Running on oeis4.)