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%I #24 Mar 19 2023 10:33:47
%S 1,19,103,463,1951,7999,32383,130303,522751,2094079,8382463,33542143,
%T 134193151,536821759,2147385343,8589737983,34359345151,137438167039,
%U 549754241023,2199020109823,8796086730751,35184359505919,140737463189503
%N a(n) = 2^(2*n+1) - 3*2^n - 1.
%C Binary numbers of the form (n)00(m) where n and m are the number of 1's, m is the index and n=m-1.
%H Vincenzo Librandi, <a href="/A195460/b195460.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = 2*a(n-1)+A052539(n) = a(n-1)+A103897(n) for n>1.
%F G.f.: x*(1+12*x-16*x^2)/((1-x)*(1-2*x)*(1-4*x)). - _Bruno Berselli_, Sep 19 2011
%e First few terms in binary are 1, 10011, 1100111, 111001111, 11110011111, 1111100111111.
%o (PARI) a(n)=1<<(2*n+1)-3<<n-1 \\ _Charles R Greathouse IV_, Sep 19 2011
%o (Magma) [2*4^n-3*2^n-1: n in [1..23]]; // _Bruno Berselli_, Sep 19 2011
%Y Cf. A052539, A103897, A195461 (prime values).
%K nonn,easy
%O 1,2
%A _Brad Clardy_, Sep 18 2011
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