A372884 - OEIS

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

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OFFSET

3,2

LINKS

Table of n, a(n) for n=3..30.

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).

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.