A084247 a(n) = -a(n-1) + 2*a(n-2), a(0)=1, a(1)=2.

1, 2, 0, 4, -4, 12, -20, 44, -84, 172, -340, 684, -1364, 2732, -5460, 10924, -21844, 43692, -87380, 174764, -349524, 699052, -1398100, 2796204, -5592404, 11184812, -22369620, 44739244, -89478484, 178956972, -357913940, 715827884, -1431655764, 2863311532

Offset: 0

Author

Paul Barry, May 23 2003

Keywords

• easy
• sign

Comments

Row sums of triangle in A112555. - Philippe Deléham, Sep 21 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2).

Crossrefs

Cf. A077925, A078008, A084246, A112555, A151575.

Programs

Magma

[(4-(-2)^n)/3: n in [0..40]]; // Vincenzo Librandi, Aug 13 2011

Mathematica

LinearRecurrence[{-1,2},{1,2},40] (* Harvey P. Dale, Nov 05 2016 *)

PARI

Vec((1+3*x)/((1-x)*(1+2*x)) + O(x^40)) \\ Michel Marcus, Feb 25 2016

SageMath

[(4-(-2)^n)/3 for n in range(41)] # G. C. Greubel, Apr 24 2023

Formula

Binomial transform of A084246.

a(n) = A077925(n-1) + 1.

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

G.f.: (1+3*x)/((1-x)*(1+2*x)).

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

a(n) = (-1)^(n+1)*(A078008(n+1) - A078008(n)). - Paul Curtz, Jun 30 2008, Feb 24 2021

a(n) = -2*a(n-1) + 4 . - Philippe Deléham, Sep 15 2009

a(n+1) = 2*A151575(n). - Philippe Deléham, Sep 21 2009

a(n) = A077925(n) + 3*A077925(n-1). - R. J. Mathar, Feb 24 2021