#JavaScript, 93 bytes
A (rather rushed) port of Nick's Python solution.
n=>(g=x=>n--?g(x<y-(-~z>>1)*6+z%2>>1?++x:(z<(y/6|0)+(-~y/6|0)?++z:z=!++y,0)):[x,y,+z])(y=z=0)
#JavaScript, 93 bytes
A (rather rushed) port of Nick's Python solution.
n=>(g=x=>n--?g(x<y-(-~z>>1)*6+z%2>>1?++x:(z<(y/6|0)+(-~y/6|0)?++z:z=!++y,0)):[x,y,+z])(y=z=0)