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

1,2

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).

Formula

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

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

Mathematica

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

Prog

(Magma) [ n le 2 select 5*n-4 else 2*Self(n-2): n in [1..42] ];
(PARI) x='x+O('x^50); Vec(x*(1+6*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 06 2017

Crossrefs

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

Sequence in context: A065174 A065284 A050088 * A015808 A112591 A106034

Adjacent sequences: A163861 A163862 A163863 * A163865 A163866 A163867

Keyword

nonn

Author

Klaus Brockhaus, Aug 05 2009

Status

approved