How many open-chain (acyclic) alkenes of molecular formula $\mathrm{C}{}_6\mathrm{H}{}_{12}$ are possible? Count structural isomers only (do not count E/Z or optical isomers) and exclude cycloalkanes. Give the answer as an integer.

Take each of the five hexane skeletons and place one C=C between adjacent carbons that each carry hydrogen. Hexane gives 3 (hex-1-, 2-, 3-ene). 2-Methylpentane gives 4 (2-methylpent-1-ene, 4-methylpent-1-ene, 2-methylpent-2-ene, 4-methylpent-2-ene). 3-Methylpentane gives 2 (3-methylpent-1-ene, 3-methylpent-2-ene) plus 2-ethylbut-1-ene, giving 3 distinct alkenes. 2,2-Dimethylbutane gives 1 (3,3-dimethylbut-1-ene) and 2,3-dimethylbutane gives 2 (2,3-dimethylbut-1-ene and -2-ene). The total is 3 + 4 + 3 + 1 + 2 = 13.