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%I #21 Sep 08 2022 08:45:38
%S 2,28,248,2032,16352,131008,1048448,8388352,67108352,536869888,
%T 4294965248,34359734272,274877898752,2199023239168,17592186011648,
%U 140737488289792,1125899906711552,9007199254478848,72057594037403648,576460752302374912,4611686018425290752
%N Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.
%C a(n) is the number whose binary representation is A138118(n).
%H G. C. Greubel, <a href="/A147537/b147537.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).
%F From _Colin Barker_, Nov 04 2012: (Start)
%F a(n) = 2^(n-1)*(4^n - 2) = 2*A147590(n).
%F a(n) = 10*a(n-1) - 16*a(n-2).
%F G.f.: 2*x*(1+4*x)/((1-2*x)*(1-8*x)). (End)
%p seq(2^n*(2^(2*n-1)-1), n = 1..20); # _G. C. Greubel_, Jan 12 2020
%t Table[FromDigits[Join[Table[1, {2n - 1}], Table[0, {n}]], 2], {n, 1, 20}] (* _Stefan Steinerberger_, Nov 11 2008 *)
%o (PARI) vector(20, n, 2^n*(2^(2*n-1)-1)) \\ _G. C. Greubel_, Jan 12 2020
%o (Magma) [2^n*(2^(2*n-1)-1): n in [1..20]] // _G. C. Greubel_, Jan 12 2020
%o (Sage) [2^n*(2^(2*n-1)-1) for n in (1..20)] # _G. C. Greubel_, Jan 12 2020
%o (GAP) List([1..20], n-> 2^n*(2^(2*n-1)-1)); # _G. C. Greubel_, Jan 12 2020
%o (Python)
%o def a(n): return ((1 << (2*n-1)) - 1) << n
%o print([a(n) for n in range(1, 22)]) # _Michael S. Branicky_, Feb 28 2021
%Y Cf. A138118.
%K base,easy,nonn
%O 1,1
%A _Omar E. Pol_, Nov 06 2008
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