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
Links
- 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).
Crossrefs
Cf. A372873.
Programs
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Mathematica
LinearRecurrence[{8,-22,24,-9},{1,4,14,50},28]
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.