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Analytical expressions of the total number of $J$ levels for three and fourfermions in a nuclear $j^n$ shell are provided. The formulas were derived usinga combination of sum rules for coefficients of fractional parentage, and"unusual" identities, i.e. which do not contain the weighting factor $(2J + 1)$involving $6j$ and $9j$ symbols.

Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage