An infinite family of triangular-number recurrences for the 3-colored partition function, plus Euler-type recurrences for 2-colored and all t-regular partition functions, derived by Rankin-Cohen bracket methods.
Andrews, The theory of partitions , Cambridge University Press, Cambridge, 1984
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Euler-type recurrences for $t$-color and $t$-regular partition functions
An infinite family of triangular-number recurrences for the 3-colored partition function, plus Euler-type recurrences for 2-colored and all t-regular partition functions, derived by Rankin-Cohen bracket methods.