Formula for the sequence 0, 1, 1, 2, 2, 3, 3, 4, 4

[darkmass]

Find a formula for the givin sequence:

0, 1 , 1 , 2 , 2 , 3 ,3 ,4 ,4 ...


thanks. any help would be appreciated.

 

[cookiemonster]

$$a_{2n} = a_{2n-2} + 1$$
$$a_{2n+1} = a_{2n-1} + 1$$
$$a_0 = 0$$
$$a_1 = 1$$

cookiemonster

 

[Muzza]

Or a_n = floor( (n + 1)/2 ), n >= 0.