A122756 Odd-indexed terms, a(n) = 2^n. Even-indexed terms, a(n) = floor(2^n+2^(n-1)).
1, 2, 6, 8, 24, 32, 96, 128, 384, 512, 1536, 2048, 6144, 8192, 24576, 32768, 98304, 131072, 393216, 524288, 1572864, 2097152, 6291456, 8388608, 25165824, 33554432, 100663296, 134217728, 402653184, 536870912, 1610612736, 2147483648
Offset: 0
Examples
Binary.................Decimal 1............................1 10...........................2 110..........................6 1000.........................8 11000.......................24 100000......................32 1100000.....................96 10000000...................128 110000000..................384 1000000000.................512 11000000000...............1536 100000000000..............2048 1100000000000.............6144 10000000000000............8192, etc. - _Philippe Deléham_, Mar 20 2014
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,4)
Programs
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Magma
[1] cat [(5*2^n-(-2)^n)/8: n in [2..40]]; // Vincenzo Librandi, Feb 10 2018
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Mathematica
a[n_] := If[Mod[n, 2] == 0, 2^(n + 1), 2^n + 2^(n + 1)] Table[a[n], {n, 0, 30}] Join[{1, 2}, LinearRecurrence[{0, 4}, {6, 8}, 40]] (* Vincenzo Librandi, Feb 10 2018 *) -
PARI
A122756(n)=(3-bittest(n,0))<<(n-1) \\ M. F. Hasler, Feb 09 2018
Formula
a(n) = 2*A084221(n-1) for all n >= 1. [Corrected by M. F. Hasler, Feb 09 2018]
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
a(n-1) = (5*2^n - (-2)^n)/8 for n>1. - Ralf Stephan, Jul 18 2013
Extensions
Edited by N. J. A. Sloane, Dec 14 2007
Comments