Identifying a quadruply charged anion containing three carbon atoms
Sesquicarbide


A quick Google search suggests that $\ce{Li4C3}$ is a real compound, but based on what I saw in the links, it probably is not ionic in the same way that lithium acetylide $\ce{Li2C2}$ is. 

$\ce{Mg2C3}$ appears to be the formula for magnesium carbide, or at least a magnesium carbide.

A carbide is a binary compound of carbon and a less electronegative element, usually a metal or metalloid. Carbide is also a generic name for mono- and polyatomic anions containing only carbon. The following ions would all carbide ions: $\ce{C^{4-}, C2^2-, C2^{4-}, C2^{6-}, C3^{4-}, C3^{6-1}, C3^{8-}}$, etc. 

The special name of three of these carbide ions are:


$\ce{C^{4-}}$ - Methide
$\ce{C2^{2-}}$ - Acetylide
$\ce{C3^{4-}}$ - Sesquicarbide