A164587 a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.

1, 8, 2, 16, 4, 32, 8, 64, 16, 128, 32, 256, 64, 512, 128, 1024, 256, 2048, 512, 4096, 1024, 8192, 2048, 16384, 4096, 32768, 8192, 65536, 16384, 131072, 32768, 262144, 65536, 524288, 131072, 1048576, 262144, 2097152, 524288, 4194304, 1048576

Offset: 1

Author

Klaus Brockhaus, Aug 17 2009

Keywords

• nonn

Comments

Interleaving of A000079 and A000079 without initial terms 1, 2, 4.

Binomial transform is A048696. Second binomial transform is A164298.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 2).

Crossrefs

Equals A112032 without initial term 4.

Cf. A000079 (powers of 2), A048696, A164298.

Programs

Magma

[ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];

Mathematica

CoefficientList[Series[(1 - x)/(1 - 10*x + 17*x^2), {x,0,50}], x] (* G. C. Greubel, Aug 12 2017 *)

PARI

x='x+O('x^50); Vec(x*(1+8*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 12 2017

Formula

a(n) = (5 + 3*(-1)^n)*2^((2*n -5 +(-1)^n)/4).

G.f.: x*(1+8*x)/(1-2*x^2).

E.g.f.: 4*cosh(sqrt(2)*x) + (1/sqrt(2))*sinh(sqrt(2)*x) - 4. - G. C. Greubel, Aug 12 2017