I think you shouldn't apply the "general alkyne formula" in the case of multiple triple bonds. Look at it this way:
* For alkane, the formula is C
nH
2n+2* Remove 2 hydrogen atoms to form a double bond, you get the alkene C
nH
2n* Remove 2 more hydrogen atoms to form either a triple bond (alkyne) or 2 double bonds (di-alkene), you get the formula C
nH
2n-2* Remove another 2 hydrogens to form either 3 double bonds (tri-alkene) or one triple + one double bonds (alken-yne), you get C
nH
2n-4* Finally, remove 2 more hydrogens to form 2 triple bonds (di-alkyne), 1 triple and 2 double bonds (alk-dien-yne) or 4 double bonds (tetra-alkene)
C
nH
2n-6Following this reasoning, for 3 triple bonds you have C
nH
2n-10.
It is better to understand where this kind of formula come from, so you don't try to use them for cases where they don't apply.