A128063 Hankel transform of A115962.

1, 2, 0, -8, -16, -32, -64, 0, 256, 512, 1024, 2048, 0, -8192, -16384, -32768, -65536, 0, 262144, 524288, 1048576, 2097152, 0, -8388608, -16777216, -33554432, -67108864, 0, 268435456, 536870912, 1073741824, 2147483648, 0, -8589934592, -17179869184

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Formula

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));

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

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

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

Crossrefs

Cf. A099443, A115962.

Sequence in context: A186033 A120559 A120555 * A171552 A087205 A319196

Adjacent sequences: A128060 A128061 A128062 * A128064 A128065 A128066

Keyword

easy,sign

Author

Paul Barry, Feb 13 2007

Status

approved