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

1,1

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A138119.

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

Sequence in context: A174668 A302444 A121213 * A180388 A288270 A221653

Adjacent sequences: A147535 A147536 A147537 * A147539 A147540 A147541

Keyword

base,easy,nonn

Author

Omar E. Pol, Nov 06 2008

Extensions

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

Status

approved