%I #41 Jan 01 2024 11:51:18
%S 1,2,6,8,24,32,96,128,384,512,1536,2048,6144,8192,24576,32768,98304,
%T 131072,393216,524288,1572864,2097152,6291456,8388608,25165824,
%U 33554432,100663296,134217728,402653184,536870912,1610612736,2147483648
%N Odd-indexed terms, a(n) = 2^n. Even-indexed terms, a(n) = floor(2^n+2^(n-1)).
%C Row sums of triangle A133569. - _Gary W. Adamson_, Sep 16 2007
%H Vincenzo Librandi, <a href="/A122756/b122756.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 (0,4)
%F a(n) = 2*A084221(n-1) for all n >= 1. [Corrected by _M. F. Hasler_, Feb 09 2018]
%F a(0)=1, a(1)=2, a(2)=6, a(n)=4*a(n-2) for n>=3. G.f.: (1+2*x+2*x^2)/(1-4*x^2). - _Philippe Deléham_, Dec 14 2007
%F a(n-1) = (5*2^n - (-2)^n)/8 for n>1. - _Ralf Stephan_, Jul 18 2013
%F a(2*n) = A164908(n), a(2*n+1) = A004171(n). - _Philippe Deléham_, Mar 20 2014
%e Binary.................Decimal
%e 1............................1
%e 10...........................2
%e 110..........................6
%e 1000.........................8
%e 11000.......................24
%e 100000......................32
%e 1100000.....................96
%e 10000000...................128
%e 110000000..................384
%e 1000000000.................512
%e 11000000000...............1536
%e 100000000000..............2048
%e 1100000000000.............6144
%e 10000000000000............8192, etc. - _Philippe Deléham_, Mar 20 2014
%t a[n_] := If[Mod[n, 2] == 0, 2^(n + 1), 2^n + 2^(n + 1)] Table[a[n], {n, 0, 30}]
%t Join[{1, 2}, LinearRecurrence[{0, 4}, {6, 8}, 40]] (* _Vincenzo Librandi_, Feb 10 2018 *)
%o (PARI) A122756(n)=(3-bittest(n,0))<<(n-1) \\ _M. F. Hasler_, Feb 09 2018
%o (Magma) [1] cat [(5*2^n-(-2)^n)/8: n in [2..40]]; // _Vincenzo Librandi_, Feb 10 2018
%Y Cf. A000079, A004171, A084221, A133569, A164908.
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, Sep 21 2006
%E Edited by _N. J. A. Sloane_, Dec 14 2007