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A143096 a(n) = 2*a(n-1)-1, with a(1)=1, a(2)=4, a(3)=5.

%I A143096 #22 May 21 2025 23:36:58
%S A143096 1,4,5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537,
%T A143096 131073,262145,524289,1048577,2097153,4194305,8388609,16777217,
%U A143096 33554433,67108865,134217729,268435457,536870913,1073741825,2147483649,4294967297,8589934593
%N A143096 a(n) = 2*a(n-1)-1, with a(1)=1, a(2)=4, a(3)=5.
%H A143096 Vincenzo Librandi, <a href="/A143096/b143096.txt">Table of n, a(n) for n = 1..2000</a>
%H A143096 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A143096 Binomial transform of 0, 1, 2, -4, 9, -13, 20, -26, 35, ... (offset 0).
%F A143096 O.g.f.: x*(1+x-5*x^2+2*x^3)/((1-x)*(1-2*x)). a(n) = 1+2^(n-1), n>2. - _R. J. Mathar_, Jul 31 2008
%F A143096 a(n) = A048578(n-2), n>=3. - _R. J. Mathar_, Aug 10 2008
%e A143096 a(4) = 9 = 2*a(3) - 1 = 2*5 - 1.
%e A143096 a(4) = 9 = (1, 3, 3, 1) dot (1, 3, -2, 5) = (1 + 9 - 6 + 5).
%t A143096 Join[{1,4},NestList[2#-1&,5,40]] (* or *) Join[{1,4},LinearRecurrence[ {3,-2},{5,9},40]] (* _Harvey P. Dale_, Feb 18 2014 *)
%Y A143096 Cf. A065190.
%Y A143096 Essentially the same as A083318, A048578 and A000051.
%K A143096 nonn,easy
%O A143096 1,2
%A A143096 _Gary W. Adamson_ and _Roger L. Bagula_, Jul 23 2008