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

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.

Mathematica

LinearRecurrence[{8, -22, 24, -9}, {1, 3, 10, 35}, 28]

Crossrefs

Cf. A007051, A372868, A372872.

Sequence in context: A112107 A381355 A187925 * A094855 A371301 A243871

Adjacent sequences: A372849 A372850 A372851 * A372853 A372854 A372855

Keyword

nonn,easy

Author

Stefano Spezia, May 15 2024

Status

approved