A167291 a(n) = A137505(2n) + A137505(2n+1).

2, 2, 0, 0, 8, 8, -24, -24, 104, 104, -408, -408, 1640, 1640, -6552, -6552, 26216, 26216, -104856, -104856, 419432, 419432, -1677720, -1677720, 6710888, 6710888, -26843544, -26843544, 107374184, 107374184, -429496728, -429496728, 1717986920, 1717986920

Offset: 0

Author

Paul Curtz, Nov 01 2009

Keywords

• easy
• sign

Comments

The formula for the singular sequence, i.e., just each unique term of the sequence (without duplication), is: a(n) = 1/10 (16-(-4)^n). - Harvey P. Dale, Jun 12 2013

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-4,4)

Programs

Mathematica

CoefficientList[Series[(-2-6x^2)/((x-1)(4x^2+1)),{x,0,50}],x] (* or *) LinearRecurrence[{1,-4,4},{2,2,0},50] (* Harvey P. Dale, Jun 12 2013 *)

Formula

a(2n) = a(2n+1) = 2*(-1)^n*A109499(n).

G.f. ( -2-6*x^2 ) / ( (x-1)*(4*x^2+1) ). - R. J. Mathar, Feb 06 2011

a(0)=2, a(1)=2, a(2)=0, a(n) = a(n-1)-4*a(n-2)+4*a(n-3). - Harvey P. Dale, Jun 12 2013