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A372878
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a(n) is the sum of all symmetric valleys in the set of flattened Catalan words of length n.
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1
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1, 7, 33, 133, 496, 1770, 6142, 20902, 70107, 232489, 763927, 2491107, 8071234, 26007364, 83402988, 266351548, 847482277, 2687729595, 8499036925, 26804655025, 84336597636, 264777690382, 829636763338, 2594821366338, 8102197327711, 25259791668925, 78638974063827
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OFFSET
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4,2
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COMMENTS
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The g.f. listed in Baril et al. has a mistake in the numerator: the factor (1 + 2*x) should be (1 - 2*x).
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LINKS
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Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 18.
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FORMULA
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From Baril et al.: (Start)
G.f.: x^4*(1 - 2*x)/((1 - 3*x)^2*(1 - x)^3).
a(n) = (3^n*(2*n - 5) - 18*n^2 + 54*n - 27)/144. (End)
E.g.f.: (32 + exp(3*x)*(6*x - 5) - 9*exp(x)*(2*x^2 - 4*x + 3))/144.
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MATHEMATICA
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LinearRecurrence[{9, -30, 46, -33, 9}, {1, 7, 33, 133, 496}, 28]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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