A147590 Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0.

1, 14, 124, 1016, 8176, 65504, 524224, 4194176, 33554176, 268434944, 2147482624, 17179867136, 137438949376, 1099511619584, 8796093005824, 70368744144896, 562949953355776, 4503599627239424, 36028797018701824, 288230376151187456

Offset

1,2

Comments

a(n) is the number whose binary representation is A147589(n).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (10,-16).

Formula

a(n) = A147537(n)/2.

From R. J. Mathar, Jul 13 2009: (Start)

a(n) = 8^n/4 - 2^(n-1) = A083332(2n-2).

a(n) = 10*a(n-1) - 16*a(n-2).

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

From César Aguilera, Jul 26 2019: (Start)

Lim_{n->infinity} a(n)/a(n-1) = 8;

a(n)/a(n-1) = 8 + 6/A083420(n). (End)

E.g.f.: (1/4)*(exp(2*x)*(-2 + exp(6*x)) + 1). - Stefano Spezia, Aug 05 2019

a(n) = A020540(n - 1)/4. - Jon Maiga, Aug 05 2019

Example

     1_10 is 1_2;
    14_10 is 1110_2;
   124_10 is 1111100_2;
  1016_10 is 1111111000_2.

Maple

seq(8^n/4-2^(n-1), n=1..25); # Nathaniel Johnston, Apr 30 2011

Mathematica

LinearRecurrence[{10, -16}, {1, 14}, 30] (* Harvey P. Dale, Oct 10 2014 *)
Table[8^n / 4 - 2^(n - 1), {n, 25}] (* Vincenzo Librandi, Jul 27 2019 *)

Prog

(Magma) [8^n/4-2^(n-1): n in [1..25]]; // Vincenzo Librandi, Jul 27 2019
(PARI) vector(25, n, 2^(n-2)*(4^n-2)) \\ G. C. Greubel, Jul 27 2019
(Sage) [2^(n-2)*(4^n-2) for n in (1..25)] # G. C. Greubel, Jul 27 2019
(GAP) List([1..25], n-> 2^(n-2)*(4^n-2)); # G. C. Greubel, Jul 27 2019

Crossrefs

Cf. A020540, A138118, A147537, A147589.

Sequence in context: A167567 A188411 A125377 * A167602 A212234 A155637

Adjacent sequences: A147587 A147588 A147589 * A147591 A147592 A147593

Keyword

base,easy,nonn

Author

Omar E. Pol, Nov 08 2008

Extensions

More terms from R. J. Mathar, Jul 13 2009

Typo in a(12) corrected by Omar E. Pol, Jul 20 2009

Status

approved