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A147539 Numbers whose binary representation is the concatenation of n 1's, 2n-1 digits 0 and n 1's.

%I A147539 #21 Sep 08 2022 08:45:38
%S A147539 5,99,1799,30735,507935,8257599,133169279,2139095295,34292630015,
%T A147539 549218943999,8791798056959,140703128621055,2251524935786495,
%U A147539 36026597995724799,576443160117411839,9223231299366486015
%N A147539 Numbers whose binary representation is the concatenation of n 1's, 2n-1 digits 0 and n 1's.
%C A147539 a(n) is the number whose binary representation is A138120(n).
%H A147539 G. C. Greubel, <a href="/A147539/b147539.txt">Table of n, a(n) for n = 1..800</a>
%H A147539 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (27,-202,432,-256).
%F A147539 a(n) = 2^n - 1 + 2^(4*n-1) - 2^(3*n-1). - _R. J. Mathar_, Nov 09 2008
%F A147539 G.f.: x*(5 -36*x +136*x^2)/((1-x)*(1-2*x)*(1-8*x)*(1-16*x)). - _Colin Barker_, Nov 04 2012
%F A147539 a(n) = 27*a(n-1) - 202*a(n-2) + 432*a(n-3) - 256*a(n-4). - _Wesley Ivan Hurt_, Jan 11 2017
%p A147539 A147539:=n->2^n-1+2^(4*n-1)-2^(3*n-1): seq(A147539(n), n=1..30); # _Wesley Ivan Hurt_, Jan 11 2017
%t A147539 Table[FromDigits[Join[Table[1, {n}], Table[0, {2n - 1}], Table[1, {n}]], 2], {n, 1, 20}] (* _Stefan Steinerberger_, Nov 11 2008 *)
%t A147539 LinearRecurrence[{27,-202,432,-256},{5,99,1799,30735},20] (* _Harvey P. Dale_, Aug 28 2017 *)
%o A147539 (Magma) [2^n-1+2^(4*n-1)-2^(3*n-1) : n in [1..20]]; // _Wesley Ivan Hurt_, Jan 11 2017
%o A147539 (PARI) vector(20, n, 2^(4*n-1) -2^(3*n-1) +2^n -1) \\ _G. C. Greubel_, Jan 12 2020
%o A147539 (Sage) [2^(4*n-1) -2^(3*n-1) +2^n -1 for n in (1..20)] # _G. C. Greubel_, Jan 12 2020
%o A147539 (GAP) List([1..20], n-> 2^(4*n-1) -2^(3*n-1) +2^n -1); # _G. C. Greubel_, Jan 12 2020
%Y A147539 Cf. A138120.
%K A147539 base,easy,nonn
%O A147539 1,1
%A A147539 _Omar E. Pol_, Nov 06 2008
%E A147539 Extended by _R. J. Mathar_ and _Stefan Steinerberger_, Nov 09 2008