A083086 a(n) = (2^(n+1) + (-4)^n)/3.

1, 0, 8, -16, 96, -320, 1408, -5376, 22016, -87040, 350208, -1396736, 5595136, -22364160, 89489408, -357892096, 1431699456, -5726535680, 22906667008, -91625619456, 366504574976, -1466014105600, 5864064811008, -23456242466816, 93825003421696, -375299946577920

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• sign
• easy

Comments

Binomial transform of A083085.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,8).

Crossrefs

Cf. A000079, A078008, A083085, A083216.

Programs

Magma

[(2*2^n+(-4)^n)/3: n in [0..30]]; // Vincenzo Librandi, Nov 12 2011

Mathematica

LinearRecurrence[{-2,8}, {1,0}, 41] (* G. C. Greubel, Feb 19 2023 *)

PARI

a(n)=(2*2^n+(-4)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

SageMath

[(2^(n+1)+(-4)^n)/3 for n in range(41)] # G. C. Greubel, Feb 19 2023

Formula

a(n) = (2*2^n + (-4)^n)/3.

G.f.: (1+2*x)/((1+4*x)*(1-2*x)).

E.g.f.: (2*exp(2*x) + exp(-4*x))/3.

a(n) = (-1)^n*A000079(n)*A078008(n). - Paul Barry, Feb 12 2004

a(n) = -2*a(n-1) + 8*a(n-2). - Vincenzo Librandi, Nov 12 2011