A372884 a(n) is the sum of all symmetric peaks in the set of flattened Catalan words of length n.
1, 5, 19, 67, 230, 778, 2602, 8618, 28303, 92275, 298949, 963253, 3089020, 9864896, 31388260, 99545572, 314779181, 992765041, 3123577735, 9806581175, 30727287586, 96104495110, 300081382574, 935547839662, 2912554595035, 9055397013503, 28119390725977, 87217771234633
Offset: 3
Links
- Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 22.
- Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-33,9).
Programs
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Mathematica
LinearRecurrence[{9,-30,46,-33,9},{1,5,19,67,230},28]
Formula
From Baril et al.: (Start)
G.f.: (1 - 2*x)^2*x^3/((1 - 3*x)^2*(1 - x)^3).
a(n) = (63 + 3^n + 2*(3^n - 45)*n + 18*n^2)/144. (End)
E.g.f.: (exp(3*x)*(1 + 6*x) + 9*exp(x)*(7 - 8*x + 2*x^2) - 64)/144.