A372872 a(n) is the total number of runs of weak ascents over all flattened Catalan words of length n.

1, 2, 6, 20, 67, 222, 728, 2368, 7653, 24602, 78730, 250956, 797159, 2524342, 7971612, 25110584, 78918985, 247518642, 774840974, 2421378052, 7554699531, 23535794702, 73222472416, 227512682160, 706073841197, 2188828907722, 6778308875538, 20970393083708, 64817578622383

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 10.

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

Formula

From Baril et al.: (Start)

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

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

E.g.f.: (exp(3*x)*(5 + 3*x) - 9*exp(x)*(x - 3) - 32)/36.

Mathematica

LinearRecurrence[{8, -22, 24, -9}, {1, 2, 6, 20}, 29]

Crossrefs

Cf. A372852, A372868.

Sequence in context: A108627 A193234 A285197 * A148475 A148476 A148477

Adjacent sequences: A372867 A372868 A372871 * A372873 A372874 A372875

Keyword

nonn,easy

Author

Stefano Spezia, May 15 2024

Status

approved