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A372884
a(n) is the sum of all symmetric peaks in the set of flattened Catalan words of length n.
2
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
3,2
LINKS
Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 22.
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.
MATHEMATICA
LinearRecurrence[{9, -30, 46, -33, 9}, {1, 5, 19, 67, 230}, 28]
CROSSREFS
Sequence in context: A347311 A121525 A163872 * A035344 A114277 A104496
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, May 15 2024
STATUS
approved