A139790 a(n) = (5*2^(n+2) - 3*n*2^n - 2*(-1)^n) / 18.

1, 2, 3, 5, 7, 9, 7, -7, -57, -199, -569, -1479, -3641, -8647, -20025, -45511, -101945, -225735, -495161, -1077703, -2330169, -5009863, -10718777, -22835655, -48467513, -102527431, -216239673, -454848967, -954437177, -1998352839, -4175662649, -8709239239

Offset: 0

Author

Paul Curtz, May 21 2008

Keywords

• sign
• easy

Comments

Binomial transform of 1,1,0,1,-2,3,-8,13,-30,... (see A113954 and A103196). - R. J. Mathar, Feb 11 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-4)

Crossrefs

Cf. A136298, A136299.

Programs

Magma

[(5*2^(n+2)-3*n*2^n-2*(-1)^n) / 18: n in [0..35]]; // Vincenzo Librandi, Aug 09 2011

Mathematica

LinearRecurrence[{3,0,-4},{1,2,3},40] (* Harvey P. Dale, May 27 2018 *)

Formula

a(n+1) - 2*a(n) = -A001045(n).

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

a(n) = 3*a(n-1) - 4*a(n-3).

Extensions

Definition replaced with closed formula by R. J. Mathar, Feb 11 2010