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

Author

Reinhard Zumkeller, Oct 16 2001

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Haskell

a064680 n = a064680_list !! n
a064680_list = zipWith ($) (cycle [(`div` 2), (* 2)]) [0..]
-- Reinhard Zumkeller, Jul 25 2012

Magma

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

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 *)
LinearRecurrence[{0,2,0,-1},{0,2,1,6},80] (* Harvey P. Dale, Mar 31 2025 *)

PARI

a(n) = if (n%2, 2*n, n/2); \\ Harry J. Smith, Sep 22 2009

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)