A147538 Numbers whose binary representation is the concatenation of n 1's and 2n-1 digits 0.

2, 24, 224, 1920, 15872, 129024, 1040384, 8355840, 66977792, 536346624, 4292870144, 34351349760, 274844352512, 2198889037824, 17591649173504, 140735340871680, 1125891316908032, 9007164895002624, 72057456598974464, 576460202547609600

Offset: 1

Author

Omar E. Pol, Nov 06 2008

Keywords

• base
• easy
• nonn

Comments

a(n) is the number whose binary representation is A138119(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-32).

Crossrefs

Cf. A138119.

Cf. A016152. - Omar E. Pol, Nov 13 2008

Programs

GAP

List([1..20], n-> 2^(2*n-1)*(2^n -1)); # G. C. Greubel, Jan 12 2020

Magma

[2^(2*n-1)*(2^n -1): n in [1..20]]; // G. C. Greubel, Jan 12 2020

Maple

seq(2^(2*n-1)*(2^n -1), n=1..20); # G. C. Greubel, Jan 12 2020

Mathematica

Table[FromDigits[Join[Table[1, {n}], Table[0, {2n - 1}]], 2], {n, 1, 20}] (* Stefan Steinerberger, Nov 11 2008 *)

PARI

vector(20, n, 2^(2*n-1)*(2^n -1)) \\ G. C. Greubel, Jan 12 2020

Python

def a(n): return ((1 << n) - 1) << (2*n-1)
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Feb 24 2021

Sage

[2^(2*n-1)*(2^n -1) for n in (1..20)] # G. C. Greubel, Jan 12 2020

Formula

a(n) = 2^(2*n-1)*(2^n -1) = A081294(n)*A000225(n). - R. J. Mathar, Nov 09 2008

a(n) = 2*A016152(n). - Omar E. Pol, Nov 13 2008

From Colin Barker, Nov 04 2012: (Start)

a(n) = 12*a(n-1) - 32*a(n-2).

G.f.: 2*x/((1-4*x)*(1-8*x)). (End)

Extensions

Extended by R. J. Mathar and Stefan Steinerberger, Nov 09 2008