2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101378We find a relationship between coefficients of fractional parentage (cfp) obtained on the one hand from the principal parent method and on the other hand from a seniority classification. We apply this to the Redmond recursion formula which relates $n \to n+1$ cfp's to $n-1 \to n$ cfp's where the principal parent classification is used. We transform this to the seniority scheme. Our formula differs from the Redmond formula inasmuch as we have a sum over the possible seniorities for the $n \to n+1$ cfp's, whereas Redmond has only one term.RevTex4, 17 pages; added Appendix A, with proof for the new relation; corrected Eqs.(26),(38), and (39)Nuclear Theorytext