A164073 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 3.

1, 3, 2, 6, 4, 12, 8, 24, 16, 48, 32, 96, 64, 192, 128, 384, 256, 768, 512, 1536, 1024, 3072, 2048, 6144, 4096, 12288, 8192, 24576, 16384, 49152, 32768, 98304, 65536, 196608, 131072, 393216, 262144, 786432, 524288, 1572864, 1048576, 3145728, 2097152, 6291456

Offset

1,2

Comments

Interleaving of A000079 and A007283.

Binomial transform is A048654. Second binomial transform is A111567. Third binomial transform is A081179 without initial 0. Fourth binomial transform is A164072. Fifth binomial transform is A164031.

Absolute second differences are the sequence itself. - Eric Angelini, Jul 30 2013

Least number having n - 1 Gaussian prime factors, counted with multiplicity, excluding units. See A239628 for a similar sequence. - T. D. Noe, Mar 31 2014

Writing the prime factorizations of the terms of this sequence, the exponents of prime factor 2 give the integers repeated (A004526), while the exponents of prime factor 3 give the sequence of alternating 0's and 1's (A000035). - Alonso del Arte, Nov 30 2016

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

G.f.: x*(1 + 3 * x)/(1 - 2 * x^2).

a(n) = A074323(n), n>=1.

a(n) = A162255(n-1), n>=2.

a(n) = A072946(n-2), n > 2. - R. J. Mathar, Aug 17 2009

a(n+3) = a(n + 2) * a(n + 1)/a(n). - Reinhard Zumkeller, Mar 04 2011

a(n) = (2/3)a(n - 1) for odd n > 1, a(n) = 3a(n - 1) for even n. - Alonso del Arte, Nov 30 2016

Mathematica

terms = 50; CoefficientList[Series[x * (1 + 3 * x)/(1 - 2 * x^2), {x, 0, terms}], x] (* T. D. Noe, Mar 31 2014 *)
Flatten[Table[{2^n, 3 * 2^n}, {n, 0, 31}]] (* Alonso del Arte, Nov 30 2016 *)
CoefficientList[Series[x (1 + 3 x)/(1 - 2 x^2), {x, 0, 44}], x] (* Michael De Vlieger, Dec 13 2016 *)

Prog

(Magma) [ n le 2 select 2*n-1 else 2*Self(n-2): n in [1..42] ];
(PARI) a(n) = (5 + (-1)^n) * 2^((2*n-9)\/4)
(PARI) Vec(x*(1+3*x)/(1-2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Dec 13 2016

Crossrefs

Cf. A000079 (powers of 2), A007283 (3*2^n), A074323, A162255, A048654, A111567, A081179, A164072, A164031, A239628.

Sequence in context: A116626 A074323 A162255 * A286595 A348404 A218615

Adjacent sequences: A164070 A164071 A164072 * A164074 A164075 A164076

Keyword

nonn,easy

Author

Klaus Brockhaus, Aug 09 2009

Status

approved