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(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
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