A078069 Expansion of (1-x)/(1+2*x+2*x^2).

1, -3, 4, -2, -4, 12, -16, 8, 16, -48, 64, -32, -64, 192, -256, 128, 256, -768, 1024, -512, -1024, 3072, -4096, 2048, 4096, -12288, 16384, -8192, -16384, 49152, -65536, 32768, 65536, -196608, 262144, -131072, -262144, 786432, -1048576, 524288, 1048576, -3145728, 4194304, -2097152, -4194304

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Pisano period lengths: 1, 1, 8, 1, 4, 8, 24, 1, 24, 4, 40, 8, 12, 24, 8, 1, 16, 24, 72, 4,... - R. J. Mathar, Aug 10 2012

Links

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

Crossrefs

Cf. A090131.

Programs

Mathematica

CoefficientList[Series[(1-x)/(1+2x+2x^2),{x,0,50}],x] (* or *) LinearRecurrence[{-2,-2},{1,-3},50] (* Harvey P. Dale, Jan 19 2012 *)

PARI

Vec((1-x)/(1+2*x+2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(n) = (-2)*(a(n-1)+a(n-2)), n>1 ; a(0)=1, a(1)=-3. - Philippe Deléham, Nov 19 2008

a(n) = A108520(n)-A108520(n-1). - R. J. Mathar, Aug 11 2012

G.f.: G(0)*(1 - x)/(2*(1 + x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 20 2013

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