A372874 a(n) is the total number of runs of descents over all flattened Catalan words of length n.

1, 4, 14, 50, 179, 632, 2192, 7478, 25157, 83660, 275570, 900506, 2922935, 9433088, 30292148, 96855134, 308501513, 979312916, 3099363926, 9782367362, 30799928891, 96758267144, 303350242904, 949277053190, 2965510133069, 9249567319772, 28807812721082, 89600770448618

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 pp. 11-12.

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

Formula

From Baril et al.: (Start)

G.f.: x*(1 - 4*x + 4*x^2 + 2*x^3)/((1 - x)^2*(1 - 3*x)^2).

a(n) = (27*n - 9 + (5*n + 1)*3^n)/36. (End)

E.g.f.: (8 + 9*exp(x)*(3*x - 1) + exp(3*x)*(15*x+1))/36.

Mathematica

LinearRecurrence[{8, -22, 24, -9}, {1, 4, 14, 50}, 28]

Crossrefs

Cf. A372873.

Sequence in context: A229314 A055099 A335921 * A153367 A211304 A047065

Adjacent sequences: A372871 A372872 A372873 * A372875 A372876 A372877

Keyword

nonn,easy

Author

Stefano Spezia, May 15 2024

Status

approved