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$$\Gamma_{\mu|\nu\sigma} = -{1\over 2} ( -\dot{A} l_{000} - A'(l_{001} + l_{010} -l_{100}) $$ $$+ \dot{B} (l_{110} + l_{101} - l_{011}) + B' l_{111}$$ $$+ \dot{C}(l_{220} + l_{202} - l_{022}) + C'(l_{221} + l_{212} + l_{122}) )$$

$$\Gamma_{\mu|\nu\sigma} = -{1\over 2} ( -\dot{A} l_{000} - A'(l_{001} + l_{010} -l_{100}) $$ $$+ \dot{B} (l_{110} + l_{101} - l_{011}) + B' l_{111}$$ $$+ \dot{C}(l_{220} + l_{202} - l_{022}) + C'(l_{221} + l_{212} - l_{122}) )$$

$$P_{i|jk} = Q_{ij|k} + Q{ik|j} - Q{jk|i}$$

$$\Gamma^\mu_{\nu\sigma} = {\dot{A}\over 2A} l^0_{00} - {A'\over 2A} (l^0_{01} + l^0_{10}) - {A'\over 2B} l^0_{11} + {\dot{B}\over 2B}(l^1_{10} + l^1_{01}) - {\dot{B}\over 2B}l^0_{11} + {B'\over 2B} l_{111} +... $$

$$P_{i|jk} = Q_{ij|k} + Q_{ik|j} - Q_{jk|i}$$

$$\Gamma^\mu_{\nu\sigma} = {\dot{A}\over 2A} l^0_{00} - {A'\over 2A} (l^0_{01} + l^0_{10}) - {A'\over 2B} l^1_{00} + {\dot{B}\over 2B}(l^1_{10} + l^1_{01}) - {\dot{B}\over 2A}l^0_{11} + {B'\over 2B} l_{111} +... $$

$$\Gamma_{\mu|\nu\sigma} = {-1\over 2} ( -\dot{A} l_{000} - A'(l_{001} + l_{010} -l_{100}) $$ $$+ \dot{B} (l_{110} + l_{101} - l_{011}) + B' l_{111}$$ $$+ \dot{C}(l_{220} + l_{202} - l_{022}) + C'(l_{221} + l_{212} + l_{122}) )$$

This can all be done in your head, term by term. If you get an $l$ which is $l^0_{221}$ it can't contribute to Ricci, because the bottom first and third index don't match the top, if you get $l^0_{121}$ then it is killed by antisymmetrization, etc, etc, it's all obvious, and you can do it in your head.

$$\Gamma_{\mu|\nu\sigma} = -{1\over 2} ( -\dot{A} l_{000} - A'(l_{001} + l_{010} -l_{100}) $$ $$+ \dot{B} (l_{110} + l_{101} - l_{011}) + B' l_{111}$$ $$+ \dot{C}(l_{220} + l_{202} - l_{022}) + C'(l_{221} + l_{212} + l_{122}) )$$

This can all be done in your head, term by term. If you get an $l$ which is $l^0_{221}$ it can't contribute to Ricci, because the bottom first and third index don't match the top, if you get $l^0_{121}$ then it is killed by antisymmetrization, etc, etc, it's all obvious.