number of colorings of a square knot???

Dear math helper

I need you help in the following:

The square knot is a connected sum of tow trefoil knots, one must be left-handed and the other right-handed. It is well-known that the number of colourings is a knot invariant. I know that we can colour trefoil by 9 distinct colourings, so the number of colourings of trefoil is 9. My question is what is the number of colourings of the square knot. I guess it is 18 but I am not sure.

Please help me and I am very appreciated.

Thank you in advance.

Re: number of colorings of a square knot???

That means we can color the square knot as well as the granny knot by 27 possible 3- colorings. I have not seen this formula before. Thank you so much vincisonfire