A137429 a(n) = -2*a(n-1) - 2*a(n-2), with a(0)=1 and a(1)=-4.

1, -4, 6, -4, -4, 16, -24, 16, 16, -64, 96, -64, -64, 256, -384, 256, 256, -1024, 1536, -1024, -1024, 4096, -6144, 4096, 4096, -16384, 24576, -16384, -16384, 65536, -98304, 65536, 65536, -262144, 393216, -262144, -262144, 1048576, -1572864, 1048576, 1048576, -4194304, 6291456

Offset: 0

Author

Paul Curtz, Apr 17 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,-2).

Crossrefs

Cf. A108520, A137444.

Programs

Mathematica

LinearRecurrence[{-2,-2},{1,-4},50] (* Harvey P. Dale, Mar 26 2013 *)

Formula

For n >= 4, a(n) = -4*a(n-4).

a(n) = (-1)^n*A137444(n) = A108520(n) - 2*A108520(n-1).

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

a(n) = (1/2 + 3*i/2)*(-1 + i)^n + (1/2 - 3*i/2)*(-1 - i)^n, n >= 0, where i=sqrt(-1). - Taras Goy, Apr 20 2019