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63*2^(n+1) + 1.
3

%I #22 Sep 08 2022 08:45:59

%S 127,253,505,1009,2017,4033,8065,16129,32257,64513,129025,258049,

%T 516097,1032193,2064385,4128769,8257537,16515073,33030145,66060289,

%U 132120577,264241153,528482305,1056964609,2113929217,4227858433,8455716865,16911433729,33822867457

%N 63*2^(n+1) + 1.

%C Binary numbers of form 111111(n)1 where n is the index and number of 0's.

%H Vincenzo Librandi, <a href="/A196657/b196657.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%e First few terms in binary are 1111111, 11111101, 111111001, 1111110001, 11111100001.

%t LinearRecurrence[{3,-2},{127,253},50] (* _Vincenzo Librandi_, Nov 25 2011 *)

%o (Magma) [63*2^(n+1) + 1: n in [0..100]];

%o (PARI) a(n)=126<<n+1 \\ _Charles R Greathouse IV_, Oct 06 2011

%K nonn,easy

%O 0,1

%A _Brad Clardy_, Oct 04 2011