A163864 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.

1, 6, 2, 12, 4, 24, 8, 48, 16, 96, 32, 192, 64, 384, 128, 768, 256, 1536, 512, 3072, 1024, 6144, 2048, 12288, 4096, 24576, 8192, 49152, 16384, 98304, 32768, 196608, 65536, 393216, 131072, 786432, 262144, 1572864, 524288, 3145728, 1048576, 6291456

Offset: 1

Author

Klaus Brockhaus, Aug 05 2009

Keywords

• nonn

Comments

Interleaving of A000079 and A007283 without initial 3.

Binomial transform is A048694, second binomial transform is A163613, third binomial transform is A163614, fourth binomial transform is A163615, fifth binomial transform is A163616, sixth binomial transform is A081183 without initial 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A000079 (powers of 2), A007283 (3*2^n), A048694, A163613, A163614, A163615, A163616, A081183.

Programs

Magma

[ n le 2 select 5*n-4 else 2*Self(n-2): n in [1..42] ];

Mathematica

LinearRecurrence[{0, 2}, {1, 6, 2, 12}, 50] (* G. C. Greubel, Aug 06 2017 *)

PARI

x='x+O('x^50); Vec(x*(1+6*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 06 2017

Formula

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

G.f.: x*(1+6*x)/(1-2*x^2).