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

0,4

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).

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

Mathematica

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

Prog

(Magma) &cat [[4^n, 0, 0, -2*4^n]: n in [0..20]]; // G. C. Greubel, Sep 15 2023
(SageMath) [((-2)^(n//2) + (-1)^n*2^(n//2))/2 for n in range(41)] # G. C. Greubel, Sep 15 2023

Crossrefs

Cf. A102560.

Sequence in context: A309244 A378518 A004025 * A072068 A078145 A348892

Adjacent sequences: A102558 A102559 A102560 * A102562 A102563 A102564

Keyword

easy,sign

Author

Paul Barry, Jan 14 2005

Status

approved