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 A064680 Halve every even number, double every odd number. 9

%I

%S 0,2,1,6,2,10,3,14,4,18,5,22,6,26,7,30,8,34,9,38,10,42,11,46,12,50,13,

%T 54,14,58,15,62,16,66,17,70,18,74,19,78,20,82,21,86,22,90,23,94,24,98,

%U 25,102,26,106,27,110,28,114,29,118,30,122,31,126,32,130,33,134,34,138,35

%N Halve every even number, double every odd number.

%C a(a(m)) = m for all m with GCD(m, 4) <= 2.

%H Harry J. Smith, <a href="/A064680/b064680.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F a(n) = n * 2^(2 * (n mod 2) - 1)

%F G.f.: (2+x+2x^2)/(1-x^2)^2.

%F a(n) = 2*a(n-2) -a(n-4).

%F a(n)a(n+3) = -2 + a(n+1)a(n+2).

%F a(2*n) = A001477(n) , a(1+2*n) = A016825(n). Paul Curtz , Mar 09 2011.

%F a(n) = n*(5-3*(-1)^n)/4. - Bruno Berselli, Mar 09 2011

%F a(n)= (period 4 sequence: repeat 2, 2, 1, 2) * (A060819(n)=0,1,1,3,1,5,...). Paul Curtz , Mar 10 2011.

%t f[n_] := 2^(2 Mod[n, 2] - 1) n; Array[f, 70, 0] (* Or *)

%t f[n_] := If[ OddQ@ n, 2 n, n/2]; Array[f, 71, 0] (* Or *)

%t CoefficientList[ Series[x (2 + x + 2 x^2)/(1 - x^2)^2, {x, 0, 70}], x] (* _Robert G. Wilson v_ *)

%o (PARI) { for (n = 1, 1000, if (n%2, a=2*n, a=n/2); write("b064680.txt", n, " ", a) ) } [From _Harry J. Smith_, Sep 22 2009]

%o (MAGMA) [IsEven(n) select n/2 else 2*n: n in [0..70]]; // Bruno Berselli, Mar 09 2011

%o a064680 n = a064680_list !! n

%o a064680_list = zipWith (\$) (cycle [(`div` 2), (* 2)]) [0..]

%o -- _Reinhard Zumkeller_, Jul 25 2012

%Y Cf. A026741.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Oct 16 2001

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