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 A156589 a(n) = 4^n - 2^n - 1. 2

%I

%S -1,1,11,55,239,991,4031,16255,65279,261631,1047551,4192255,16773119,

%T 67100671,268419071,1073709055,4294901759,17179738111,68719214591,

%U 274877382655,1099510579199,4398044413951,17592181850111,70368735789055

%N a(n) = 4^n - 2^n - 1.

%C Sequence A098845 lists indices of primes, i.e., a(n) prime <=> n=A098845(k) for some k.

%C Starting with n=2, binary numbers of the form (n-1)0(n) where n is the index and the number of 1's. It can also be formed by appending a 1 to the right of each term of A129868.

%C 1/a(n) = Sum_{m>0} A000045(m)*2^(-n(m+1)) for n > 0. E.g., 1/a(4) = 0.0000 0001 0001 0010 0011 0101 1000 ... in binary. - _Lee A. Newberg_, Apr 12 2018

%H Vincenzo Librandi, <a href="/A156589/b156589.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F G.f.: ( 1-8*x+10*x^2 ) / ( (-1+x)*(2*x-1)*(4*x-1) ). - _R. J. Mathar_, Oct 21 2014

%t Table[4^n - 2^n - 1, {n, 0, 25}] (* _Vincenzo Librandi_, Apr 13 2018 *)

%o (PARI) vector(99,n,4^n-2^n-1)

%o (MAGMA) [4^n-2^n-1: n in [0..30]]; // _Vincenzo Librandi_, Apr 13 2018

%Y Cf. A000045, A098845, A129868.

%K sign,easy

%O 0,3

%A _M. F. Hasler_, Feb 10 2009

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)