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
Links
- 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).
Programs
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Mathematica
LinearRecurrence[{8,-22,24,-9},{1,3,10,35},28]
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.