%I #11 Sep 08 2019 01:50:52

%S 1,2,0,-8,-16,-32,-64,0,256,512,1024,2048,0,-8192,-16384,-32768,

%T -65536,0,262144,524288,1048576,2097152,0,-8388608,-16777216,

%U -33554432,-67108864,0,268435456,536870912,1073741824,2147483648,0,-8589934592,-17179869184

%N Hankel transform of A115962.

%F a(n) = 2^n*((1/2 - 3*sqrt(5)/10)*cos(3*Pi*n/5) + sqrt(1/10 - sqrt(5)/50)*sin(3*Pi*n/5) + (3*sqrt(5)/10 + 1/2)*cos(Pi*n/5) - sqrt(sqrt(5)/50 + 1/10)*sin(Pi*n/5));

%F a(n) = 2^n*Sum_{k=0..floor((n+2)/2)} binomial(n-k+2,k)*(-1)^k*Fibonacci(n-2k+3);

%F a(n) = 2^n*A099443(n+2).

%F Empirical g.f.: -(2*x-1)*(4*x^2 + 2*x + 1) / (16*x^4 - 8*x^3 + 4*x^2 - 2*x + 1). - _Colin Barker_, Jun 28 2013

%Y Cf. A099443, A115962.

%K easy,sign

%O 0,2

%A _Paul Barry_, Feb 13 2007