A372852 - OEIS

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A372852

a(n) is the total number of runs of ascents over all flattened Catalan words of length n.

1, 3, 10, 35, 123, 427, 1460, 4923, 16405, 54131, 177150, 575731, 1860047, 5978715, 19131880, 60982859, 193710249, 613415779, 1937102450, 6101872707, 19177314211, 60147030923, 188286357660, 588394867675, 1835791987133, 5719198113747, 17793060798310, 55285581766163

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 7.

Index entries for linear recurrences with constant coefficients, signature (8,-22,24,-9).

FORMULA

From Baril et al.: (Start)

G.f.: x*(1 - 5*x + 8*x^2 - 3*x^2)/((1 - x)^2*(1 - 3*x)^2).

a(n) = (3^(n-1) + 1)*(n + 1)/4. (End)

E.g.f.: exp(x)*(exp(2*x) - 1)*(x - 2)/4.