A016724 Expansion of (2-2*x-x^2)/((1-2*x^2)*(1-x)^2).

2, 2, 5, 4, 9, 6, 15, 8, 25, 10, 43, 12, 77, 14, 143, 16, 273, 18, 531, 20, 1045, 22, 2071, 24, 4121, 26, 8219, 28, 16413, 30, 32799, 32, 65569, 34, 131107, 36, 262181, 38, 524327, 40, 1048617, 42, 2097195, 44

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

X. Gourdon and B. Salvy, Effective asymptotics of linear recurrences with rational coefficients, Discrete Mathematics, vol. 153, no. 1-3, 1996, pages 145-163.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,2).

Formula

G.f.: (2-2*x-x^2)/((1-2*x^2)*(1-x)^2).

a(2*n) = 2^n+2*n+1, a(2*n+1) = 2*n+2. - Christian Krause, Feb 04 2024

Mathematica

CoefficientList[Series[(2-2x-x^2)/(1-2x^2)/(1-x)^2, {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, -4, 2}, {2, 2, 5, 4}, 50] (* Harvey P. Dale, Jan 07 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((2-2*x-x^2)/((1-2*x^2)*(1-x)^2)) \\ G. C. Greubel, Sep 15 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((2-2*x-x^2)/((1-2*x^2)*(1-x)^2))); // G. C. Greubel, Sep 15 2018

Crossrefs

Sequence in context: A021820 A222882 A236335 * A058657 A321285 A091434

Adjacent sequences: A016721 A016722 A016723 * A016725 A016726 A016727

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved