A070876 Binary expansion is 1xx100...0 where xx = 00 or 11.

9, 15, 18, 30, 36, 60, 72, 120, 144, 240, 288, 480, 576, 960, 1152, 1920, 2304, 3840, 4608, 7680, 9216, 15360, 18432, 30720, 36864, 61440, 73728, 122880, 147456, 245760, 294912, 491520, 589824, 983040, 1179648, 1966080, 2359296, 3932160

Offset: 0

Author

N. J. A. Sloane, May 19 2002

Keywords

• nonn
• base
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A070875.

Programs

Magma

[n le 2 select 6*n+3 else 2*Self(n-2): n in [1..38]]; // Bruno Berselli, Mar 02 2011

Mathematica

a = {}; Do[a = Append[a, FromDigits[ Join[{1, 0, 0, 1}, Table[0, {n}]], 2]]; a = Append[a, FromDigits[ Join[{1, 1, 1, 1}, Table[0, {n}]], 2]], {n, 0, 20}]; a
CoefficientList[Series[3 (3 + 5 x) / (1 - 2 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{0,2},{9,15},40] (* Harvey P. Dale, Aug 06 2021 *)

PARI

my(x='x+O('x^99)); Vec(3*(3+5*x)/(1-2*x^2)) \\ Altug Alkan, Sep 20 2018

Formula

From Bruno Berselli, Mar 02 2011: (Start)

G.f.: 3*(3+5*x)/(1-2*x^2).

a(n) = 3*(4-(-1)^n)*2^((2*n+(-1)^n-1)/4). Therefore: a(n) = 9*2^(n/2) for n even, otherwise a(n) = 15*2^((n-1)/2).

a(n) = 2*a(n-2) for n>1. (End)

Sum_{n>=0} 1/a(n) = 16/45. - Amiram Eldar, Mar 28 2022

Extensions

More terms from Robert G. Wilson v, May 20 2002