A077966 Expansion of 1/(1+2*x^2).

1, 0, -2, 0, 4, 0, -8, 0, 16, 0, -32, 0, 64, 0, -128, 0, 256, 0, -512, 0, 1024, 0, -2048, 0, 4096, 0, -8192, 0, 16384, 0, -32768, 0, 65536, 0, -131072, 0, 262144, 0, -524288, 0, 1048576, 0, -2097152, 0, 4194304, 0, -8388608, 0, 16777216, 0, -33554432, 0, 67108864, 0, -134217728, 0, 268435456

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.

Inverse binomial transform of A087455. - Philippe Deléham, Dec 02 2008

Pisano period lengths: 1, 1, 2, 1, 8, 2, 12, 1, 6, 8, 10, 2, 24, 12, 8, 1, 16, 6, 18, 8,... - R. J. Mathar, Aug 10 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,-2).

Crossrefs

Cf. A000079, A077957.

Programs

GAP

a:=[1,0];; for n in [3..60] do a[n]:=-2*a[n-2]; od; a; # G. C. Greubel, Jun 24 2019

Magma

I:=[1,0]; [n le 2 select I[n] else -2*Self(n-2): n in [1..60]]; // G. C. Greubel, Jun 24 2019

Maple

A077966:=n->(1+(-1)^n)*(-2)^(n/2)/2; seq(A077966(n), n=0..50); # Wesley Ivan Hurt, Apr 02 2014

Mathematica

CoefficientList[Series[1/(1 + 2*x^2), {x,0,60}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
LinearRecurrence[{0,-2}, {1,0}, 60] (* G. C. Greubel, Jun 24 2019 *)

PARI

Vec(1/(1+2*x^2)+O(x^60)) \\ Charles R Greathouse IV, Sep 24 2012

PARI

for(n=0, 51, print1(imag(quadgen(-8)^(n+1)), ", ")) \\ Arkadiusz Wesolowski, Dec 26 2012

Sage

[lucas_number1(n,0,2) for n in range(1,60)] # Zerinvary Lajos, Jul 16 2008

Formula

a(n) = (1+(-1)^n)*(-2)^(n/2)/2. - R. J. Mathar, Apr 23 2009

a(n) = ((n+1) mod 2 )*(-2)^floor((n+1)/2). - Wesley Ivan Hurt, Apr 06 2014

E.g.f.: cos(sqrt(2)*x). - G. C. Greubel, Jun 24 2019