cp's OEIS Frontend

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

%I A147590 #49 Sep 08 2022 08:45:38
%S A147590 1,14,124,1016,8176,65504,524224,4194176,33554176,268434944,
%T A147590 2147482624,17179867136,137438949376,1099511619584,8796093005824,
%U A147590 70368744144896,562949953355776,4503599627239424,36028797018701824,288230376151187456
%N A147590 Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0.
%C A147590 a(n) is the number whose binary representation is A147589(n).
%H A147590 Nathaniel Johnston, <a href="/A147590/b147590.txt">Table of n, a(n) for n = 1..500</a>
%H A147590 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).
%F A147590 a(n) = A147537(n)/2.
%F A147590 From _R. J. Mathar_, Jul 13 2009: (Start)
%F A147590 a(n) = 8^n/4 - 2^(n-1) = A083332(2n-2).
%F A147590 a(n) = 10*a(n-1) - 16*a(n-2).
%F A147590 G.f.: x*(1+4*x)/((1-2*x)*(1-8*x)). (End)
%F A147590 From _César Aguilera_, Jul 26 2019: (Start)
%F A147590 Lim_{n->infinity} a(n)/a(n-1) = 8;
%F A147590 a(n)/a(n-1) = 8 + 6/A083420(n). (End)
%F A147590 E.g.f.: (1/4)*(exp(2*x)*(-2 + exp(6*x)) + 1). - _Stefano Spezia_, Aug 05 2019
%F A147590 a(n) = A020540(n - 1)/4. - _Jon Maiga_, Aug 05 2019
%e A147590      1_10 is 1_2;
%e A147590     14_10 is 1110_2;
%e A147590    124_10 is 1111100_2;
%e A147590   1016_10 is 1111111000_2.
%p A147590 seq(8^n/4-2^(n-1),n=1..25); # _Nathaniel Johnston_, Apr 30 2011
%t A147590 LinearRecurrence[{10,-16},{1,14},30] (* _Harvey P. Dale_, Oct 10 2014 *)
%t A147590 Table[8^n / 4 - 2^(n - 1), {n, 25}] (* _Vincenzo Librandi_, Jul 27 2019 *)
%o A147590 (Magma) [8^n/4-2^(n-1): n in [1..25]]; // _Vincenzo Librandi_, Jul 27 2019
%o A147590 (PARI) vector(25, n, 2^(n-2)*(4^n-2)) \\ _G. C. Greubel_, Jul 27 2019
%o A147590 (Sage) [2^(n-2)*(4^n-2) for n in (1..25)] # _G. C. Greubel_, Jul 27 2019
%o A147590 (GAP) List([1..25], n-> 2^(n-2)*(4^n-2)); # _G. C. Greubel_, Jul 27 2019
%Y A147590 Cf. A020540, A138118, A147537, A147589.
%K A147590 base,easy,nonn
%O A147590 1,2
%A A147590 _Omar E. Pol_, Nov 08 2008
%E A147590 More terms from _R. J. Mathar_, Jul 13 2009
%E A147590 Typo in a(12) corrected by _Omar E. Pol_, Jul 20 2009