login
A064680
Halve every even number, double every odd number.
17
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)
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
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 16 2001
STATUS
approved