#JavaScript, 93 bytes

A (rather rushed) port of [Nick's Python solution](https://codegolf.stackexchange.com/a/188283/58974).

    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)

[Try It Online!](https://tio.run/##JY1BC4IwGED/SgnBvj5ns4MH9Zv3DnXoGB3EnBiyhUpsI/rra9DtwXvwnu27Xbp5fK1cm0cfFAVNkg1kSWrOm4HZ2nHGv17KHPYF@t0xUoNoS@Zr5g7FRwDG4E9R@NLTFtGlAqC82dSl6O/AHHkSEJSZmSVR2ToXQlTQGb2Yqc8mE1eYbGiT4Ol6OWfLOo96GJVjKgoEgPAD)