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 A372878 a(n) is the sum of all symmetric valleys in the set of flattened Catalan words of length n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS The g.f. listed in Baril et al. has a mistake in the numerator: the factor (1 + 2*x) should be (1 - 2*x). LINKS Table of n, a(n) for n=4..30. Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 18. Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-33,9). FORMULA 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. a(n) - a(n-1) = A261064(n-3). MATHEMATICA LinearRecurrence[{9, -30, 46, -33, 9}, {1, 7, 33, 133, 496}, 28] CROSSREFS Cf. A261064, A371963, A371964, A372875. Sequence in context: A066810 A262600 A034577 * A141291 A278027 A225895 Adjacent sequences: A372875 A372876 A372877 * A372879 A372880 A372881 KEYWORD nonn,easy AUTHOR Stefano Spezia, May 15 2024 STATUS approved

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Last modified August 7 14:24 EDT 2024. Contains 375013 sequences. (Running on oeis4.)