A061648 Area of all nondecreasing Dyck paths of length 2n.

1, 6, 29, 122, 464, 1648, 5583, 18280, 58337, 182480, 561686, 1706136, 5125069, 15249762, 45005309, 131871638, 383966228, 1111712440, 3202612347, 9184267060, 26229945521, 74631504716, 211620269834, 598168622352, 1685884643929, 4738755368478, 13286692506173

Offset

1,2

Links

Table of n, a(n) for n=1..27.

E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.

Index entries for linear recurrences with constant coefficients, signature (10,-39,75,-75,39,-10,1).

Formula

G.f.: x*(1-4*x+8*x^2-9*x^3+2*x^5)/((1-x)*(1-3*x+x^2)^3).

a(n) = Sum_{k=1..n^2} k*A121467(n,k). - Alois P. Heinz, Mar 02 2018

Mathematica

LinearRecurrence[{10, -39, 75, -75, 39, -10, 1}, {1, 6, 29, 122, 464, 1648, 5583}, 30] (* Harvey P. Dale, Feb 16 2020 *)

Crossrefs

Cf. A121467.

Sequence in context: A006816 A184130 A326805 * A281050 A267774 A243474

Adjacent sequences: A061645 A061646 A061647 * A061649 A061650 A061651

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 14 2001

Status

approved