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A064680
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Halve every even number, double every odd number.
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9
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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, 54, 14, 58, 15, 62, 16, 66, 17, 70, 18, 74, 19, 78, 20, 82, 21, 86, 22, 90, 23, 94, 24, 98, 25, 102, 26, 106, 27, 110, 28, 114, 29, 118, 30, 122, 31, 126, 32, 130, 33, 134, 34, 138, 35
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(a(m)) = m for all m with GCD(m, 4) <= 2.
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
| a(n) = n * 2^(2 * (n mod 2) - 1)
G.f.: (2+x+2x^2)/(1-x^2)^2.
a(n) = 2*a(n-2) -a(n-4).
a(n)a(n+3) = -2 + a(n+1)a(n+2).
a(2*n) = A001477(n) , a(1+2*n) = A016825(n). Paul Curtz , Mar 09 2011.
a(n) = n*(5-3*(-1)^n)/4. - Bruno Berselli, Mar 09 2011
a(n)= (period 4 sequence: repeat 2, 2, 1, 2) * (A060819(n)=0,1,1,3,1,5,...). Paul Curtz , Mar 10 2011.
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MATHEMATICA
| f[n_] := 2^(2 Mod[n, 2] - 1) n; Array[f, 70, 0] (* Or *)
f[n_] := If[ OddQ@ n, 2 n, n/2]; Array[f, 71, 0] (* Or *)
CoefficientList[ Series[x (2 + x + 2 x^2)/(1 - x^2)^2, {x, 0, 70}], x] (* RGWv *)
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PROG
| (PARI) { for (n = 1, 1000, if (n%2, a=2*n, a=n/2); write("b064680.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 22 2009]
(MAGMA) [IsEven(n) select n/2 else 2*n: n in [0..70]]; // Bruno Berselli, Mar 09 2011
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CROSSREFS
| Cf. A026741.
Sequence in context: A076891 A071883 A099304 * A057560 A085592 A174421
Adjacent sequences: A064677 A064678 A064679 * A064681 A064682 A064683
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 16 2001
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