A102561 a(n) = 2^floor(n/2)*((-1)^floor(n/2) + (-1)^n)/2.

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

Offset: 0

Author

Paul Barry, Jan 14 2005

Keywords

• easy
• sign

Links

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

Crossrefs

Cf. A102560.

Programs

Magma

&cat [[4^n,0,0,-2*4^n]: n in [0..20]]; // G. C. Greubel, Sep 15 2023

Mathematica

LinearRecurrence[{0,0,0,4}, {1,0,0,-2}, 64] (* Georg Fischer, Sep 02 2021 *)

SageMath

[((-2)^(n//2) + (-1)^n*2^(n//2))/2 for n in range(41)] # G. C. Greubel, Sep 15 2023

Formula

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

a(n) = A102560(n)*2^floor(n/2).

a(n) = 4*a(n-4). - Georg Fischer, Sep 02 2021