A372878 a(n) is the sum of all symmetric valleys in the set of flattened Catalan words of length n.

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

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