A064680 Halve every even number, double every odd number.

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

Offset

0,2

Comments

a(a(m)) = m for all m with gcd(m, 4) <= 2.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000, (corrected by Peter Luschny, Jan 19 2019)

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(n) = n * 2^(2 * (n mod 2) - 1).

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

a(n) = 2*a(n-2) - a(n-4) for n>3.

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

E.g.f.: x*(sinh(x) + 4*cosh(x))/2. - Ilya Gutkovskiy, Jul 24 2016

a(n) = lcm(numerator(n/2), denominator(n/2)). - Wesley Ivan Hurt, Jul 24 2016

a(n) = A176447(n) + n. - Filip Zaludek, Dec 10 2016

From Amiram Eldar, Oct 07 2023: (Start)

a(n) = lcm(n,2) / gcd(n,2).

Sum_{k=1..n} a(k) ~ (5/8)*n^2. (End)

Maple

A064680:=n->n*(5-3*(-1)^n)/4: seq(A064680(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2016

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] (* Robert G. Wilson v *)

Prog

(PARI) a(n) = if (n%2, 2*n, n/2); \\ Harry J. Smith, Sep 22 2009
(Magma) [IsEven(n) select n/2 else 2*n: n in [0..70]]; // Bruno Berselli, Mar 09 2011
(Haskell)
a064680 n = a064680_list !! n
a064680_list = zipWith ($) (cycle [(`div` 2), (* 2)]) [0..]
-- Reinhard Zumkeller, Jul 25 2012

Crossrefs

Cf. A001477, A016825, A026741, A060819, A109043, A176447.

Sequence in context: A071883 A368241 A099304 * A352544 A363596 A354280

Adjacent sequences: A064677 A064678 A064679 * A064681 A064682 A064683

Keyword

nonn,easy

Author

Reinhard Zumkeller, Oct 16 2001

Status

approved