A234269 Expansion of (1-2*x^2-sqrt(1-4*x^2-4*x^3))/(2*x*sqrt(1-4*x^2-4*x^3)).

0, 0, 1, 1, 4, 7, 18, 39, 90, 206, 470, 1085, 2492, 5762, 13314, 30849, 71556, 166210, 386562, 899976, 2097524, 4892966, 11423984, 26693381, 62417940, 146053272, 341970538, 801168316, 1878016792, 4404544926, 10335098184, 24262063281, 56980852484, 133877548896

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

J.-L. Baril, J.-M. Pallo, Motzkin subposet and Motzkin geodesics in Tamari lattices, 2013.

Formula

Conjecture D-finite with recurrence: -(n+1)*(2*n-5)*a(n) -2*n*(n-4)*a(n-1) +4*(n-1)*(2*n-3)*a(n-2) +2*(8*n^2-32*n+29)*a(n-3) +4*(n-2)*(2*n-7)*a(n-4)=0. - R. J. Mathar, Jan 24 2020

Mathematica

CoefficientList[Series[(1 - 2 x^2 - Sqrt[1 - 4 x^2 - 4 x^3]) / (2 x Sqrt[1 - 4 x^2 - 4 x^3]), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 25 2020 *)

Prog

(Magma)  m:=50; R<x>:=PowerSeriesRing(Rationals(), m); [0, 0] cat  Coefficients(R!((1 - 2*x^2 - Sqrt(1 - 4*x^2 - 4*x^3)) / (2*x*Sqrt(1 - 4*x^2 - 4*x^3)))); // Vincenzo Librandi, Jan 25 2020
(PARI) seq(n)={Vec((1-2*x^2-sqrt(1-4*x^2-4*x^3 + O(x^2*x^n)))/(2*x*sqrt(1-4*x^2-4*x^3 + O(x*x^n))), -(n+1))} \\ Andrew Howroyd, Jan 25 2020

Crossrefs

Cf. A234270.

Sequence in context: A289975 A124400 A077920 * A135582 A100828 A267488

Adjacent sequences: A234266 A234267 A234268 * A234270 A234271 A234272

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2013

Extensions

Offset changed to 0 and more terms from Alois P. Heinz, Nov 16 2015

Status

approved