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
Links
- 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).
Programs
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Mathematica
LinearRecurrence[{8,-22,24,-9},{1,2,6,20},29]
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.