A102561 - OEIS

%I #13 Sep 15 2023 01:43:10

%S 1,0,0,-2,4,0,0,-8,16,0,0,-32,64,0,0,-128,256,0,0,-512,1024,0,0,-2048,

%T 4096,0,0,-8192,16384,0,0,-32768,65536,0,0,-131072,262144,0,0,-524288,

%U 1048576,0,0,-2097152,4194304,0,0,-8388608,16777216,0,0,-33554432,67108864,0,0,-134217728

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

%H G. C. Greubel, <a href="/A102561/b102561.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4).

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

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

%F a(n) = 4*a(n-4). - _Georg Fischer_, Sep 02 2021

%t LinearRecurrence[{0,0,0,4}, {1,0,0,-2}, 64] (* _Georg Fischer_, Sep 02 2021 *)

%o (Magma) &cat [[4^n,0,0,-2*4^n]: n in [0..20]]; // _G. C. Greubel_, Sep 15 2023

%o (SageMath) [((-2)^(n//2) + (-1)^n*2^(n//2))/2 for n in range(41)] # _G. C. Greubel_, Sep 15 2023

%Y Cf. A102560.

%K easy,sign

%O 0,4

%A _Paul Barry_, Jan 14 2005