|
%I #10 Sep 08 2022 08:45:38
%S 5,231,7967,260223,8372735,268306431,8588894207,274869551103,
%T 8796026044415,281474440364031,9007194961870847,288230341800361983,
%U 9223371762010423295,295147902980463788031,9444732948147641253887
%N Numbers whose binary representation is the concatenation of 2n-1 digits 1, n digits 0 and 2n-1 digits 1.
%C a(n) is the number whose binary representation is A138826(n).
%H G. C. Greubel, <a href="/A147540/b147540.txt">Table of n, a(n) for n = 1..660</a>
%F From _R. J. Mathar_, Nov 09 2008: (Start)
%F a(n) = 2^(5*n-2) - 2^(3*n-1) + 2^(2*n-1) - 1.
%F G.f.: x*(5 +6*x -128*x^2 +768*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-32*x)). (End)
%p seq( 2^(5*n-2) -2^(3*n-1) +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}], Table[1, {2n-1}]], 2], {n,15}] (* _Stefan Steinerberger_, Nov 11 2008 *)
%o (PARI) vector(20, n, 2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1) \\ _G. C. Greubel_, Jan 12 2020
%o (Magma) [2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1: n in [1..20]]; // _G. C. Greubel_, Jan 12 2020
%o (Sage) [2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1 for n in (1..20)] # _G. C. Greubel_, Jan 12 2020
%o (GAP) List([1..20], n-> 2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1); # _G. C. Greubel_, Jan 12 2020
%Y Cf. A138826.
%K base,easy,nonn
%O 1,1
%A _Omar E. Pol_, Nov 06 2008
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Nov 11 2008
| 