A164090 a(n) = 2*a(n-2) for n > 2; a(1) = 2, a(2) = 3.

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

Offset: 1

Author

Klaus Brockhaus, Aug 09 2009

Keywords

• nonn
• easy

Comments

Interleaving of A000079 without initial 1 and A007283.

Agrees from a(2) onward with A145751 for all terms listed there (up to 65536). Apparently equal to 2, 3 followed by A090989. Equals 2 followed by A163978.

Binomial transform is A000129 without first two terms, second binomial transform is A020727, third binomial transform is A164033, fourth binomial transform is A164034, fifth binomial transform is A164035.

Number of achiral necklaces or bracelets with n beads using up to 2 colors. For n=5, the eight achiral necklaces or bracelets are AAAAA, AAAAB, AAABB, AABAB, AABBB, ABABB, ABBBB, and BBBBB. - Robert A. Russell, Sep 22 2018

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), A029744, A145751, A090989, A163978, A000129, A020727, A164033, A164034, A164035, A052955, A027383, A060482, A070875.

Second column of A284855.

Programs

Magma

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

Mathematica

a[n_] := If[EvenQ[n], 3*2^(n/2 - 1), 2^((n + 1)/2)]; Array[a, 42] (* Jean-François Alcover, Oct 12 2017 *)
RecurrenceTable[{a[1]==2,a[2]==3,a[n]==2a[n-2]},a,{n,50}] (* or *) LinearRecurrence[{0,2},{2,3},50] (* Harvey P. Dale, Mar 01 2018 *)

PARI

a(n) = if(n%2,2,3) * 2^((n-1)\2); \\ Andrew Howroyd, Oct 07 2017

Formula

a(n) = A029744(n+1).

a(n) = A052955(n-1) + 1.

a(n) = A027383(n-2) + 2 for n > 1.

a(n) = A060482(n-1) + 3 for n > 3.

a(n) = A070875(n) - A070875(n-1).

a(n) = (7 - (-1)^n)*2^((1/4)*(2*n - 1 + (-1)^n))/4.

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

a(n) = A063759(n-1), n>1. - R. J. Mathar, Aug 17 2009

Sum_{n>=1} 1/a(n) = 5/3. - Amiram Eldar, Mar 28 2022