A166978 a(n) = 4*( 1-(-1)^n) -2^n.

-1, 6, -4, 0, -16, -24, -64, -120, -256, -504, -1024, -2040, -4096, -8184, -16384, -32760, -65536, -131064, -262144, -524280, -1048576, -2097144, -4194304, -8388600, -16777216, -33554424, -67108864, -134217720, -268435456, -536870904, -1073741824, -2147483640

Offset: 0

Author

Paul Curtz, Oct 26 2009

Keywords

• easy
• sign

Links

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

Programs

Magma

[4*( 1-(-1)^n) -2^n: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011

Mathematica

LinearRecurrence[{2,1,-2}, {-1, 6, -4}, 50] (* or *) Table[4*(1-(-1)^n) - 2^n, {n,0,25}] (* G. C. Greubel, May 30 2016 *)

Formula

a(n) = A166956(n+1)-3*A166956(n).

a(2n) = -A000302(n). a(2n+1) = 6*(-1)^n*A084240(n).

a(n+1) - 2*a(n) = 4*( 3*(-1)^n-1) = 8 *(-1)^n*A000034(n).

G.f.: -(5*x-1)*(3*x-1) / ( (x-1)*(2*x-1)*(1+x) ). - R. J. Mathar, Jul 01 2011

E.g.f.: 8*sinh(x) - exp(2*x). - G. C. Greubel, May 30 2016