cp's OEIS Frontend

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

%I A147538 #22 Apr 19 2023 02:26:00
%S A147538 2,24,224,1920,15872,129024,1040384,8355840,66977792,536346624,
%T A147538 4292870144,34351349760,274844352512,2198889037824,17591649173504,
%U A147538 140735340871680,1125891316908032,9007164895002624,72057456598974464,576460202547609600
%N A147538 Numbers whose binary representation is the concatenation of n 1's and 2n-1 digits 0.
%C A147538 a(n) is the number whose binary representation is A138119(n).
%H A147538 G. C. Greubel, <a href="/A147538/b147538.txt">Table of n, a(n) for n = 1..1000</a>
%H A147538 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-32).
%F A147538 a(n) = 2^(2*n-1)*(2^n -1) = A081294(n)*A000225(n). - _R. J. Mathar_, Nov 09 2008
%F A147538 a(n) = 2*A016152(n). - _Omar E. Pol_, Nov 13 2008
%F A147538 From _Colin Barker_, Nov 04 2012: (Start)
%F A147538 a(n) = 12*a(n-1) - 32*a(n-2).
%F A147538 G.f.: 2*x/((1-4*x)*(1-8*x)). (End)
%p A147538 seq(2^(2*n-1)*(2^n -1), n=1..20); # _G. C. Greubel_, Jan 12 2020
%t A147538 Table[FromDigits[Join[Table[1, {n}], Table[0, {2n - 1}]], 2], {n, 1, 20}] (* _Stefan Steinerberger_, Nov 11 2008 *)
%o A147538 (PARI) vector(20, n, 2^(2*n-1)*(2^n -1)) \\ _G. C. Greubel_, Jan 12 2020
%o A147538 (Magma) [2^(2*n-1)*(2^n -1): n in [1..20]]; // _G. C. Greubel_, Jan 12 2020
%o A147538 (Sage) [2^(2*n-1)*(2^n -1) for n in (1..20)] # _G. C. Greubel_, Jan 12 2020
%o A147538 (GAP) List([1..20], n-> 2^(2*n-1)*(2^n -1)); # _G. C. Greubel_, Jan 12 2020
%o A147538 (Python)
%o A147538 def a(n): return ((1 << n) - 1) << (2*n-1)
%o A147538 print([a(n) for n in range(1, 22)]) # _Michael S. Branicky_, Feb 24 2021
%Y A147538 Cf. A138119.
%Y A147538 Cf. A016152. - _Omar E. Pol_, Nov 13 2008
%K A147538 base,easy,nonn
%O A147538 1,1
%A A147538 _Omar E. Pol_, Nov 06 2008
%E A147538 Extended by _R. J. Mathar_ and _Stefan Steinerberger_, Nov 09 2008