A118417 a(n) = (2*n + 1) * 2^(n + 1).

2, 12, 40, 112, 288, 704, 1664, 3840, 8704, 19456, 43008, 94208, 204800, 442368, 950272, 2031616, 4325376, 9175040, 19398656, 40894464, 85983232, 180355072, 377487360, 788529152, 1644167168, 3422552064, 7113539584, 14763950080, 30601641984, 63350767616

Offset: 0

Author

Reinhard Zumkeller, Apr 27 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Cf. A014480, A118416.

Cf. A002193, A196525, A195695.

Programs

Magma

[(2*n+1)*2^(n+1): n in [0..40]]; // Vincenzo Librandi, Dec 26 2010

Mathematica

CoefficientList[Series[2 (1 - 3 x^2 + 2 x^3)/((1 - x)^2 (1 - 2 x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 02 2016 *)
Table[(2n+1)2^(n+1),{n,0,30}] (* or *) LinearRecurrence[{4,-4},{2,12},30] (* Harvey P. Dale, Oct 25 2021 *)

Formula

a(n) = A118416(n+1,n) = 2*A014480(n).

G.f.: 2*(1-3*x^2+2*x^3)/((1-x)^2*(1-2*x)^2). - Vincenzo Librandi, Sep 02 2016

Sum_{n>=0} 1/a(n) = A196525. - Fred Daniel Kline, May 24 2019

Sum_{n>=0} (-1)^n/a(n) = arctan(1/sqrt(2))/sqrt(2) = A195695 / A002193. - Amiram Eldar, Oct 01 2022