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We can interpret a(n) as the number of 2-color partitions of n with colors r and b subject to the restriction that color b appears only in even parts. For example, there are three such partitions of 2: 2r, 2b, 1r + 1r. Since a(n) is closely related to Ramanujan’s cubic continued fraction (see [4]), we will say that a(n) is the number of cubic partitions of n. In particular, by using identities for the cubic continued fraction, Chan found a result analogous to “Ramanujan’s most beautiful identity” (in the words of G. H. Hardy [17, p. xxxv]), namely, ∞ ∑

An analog of crank for a certain kind of partition function arising from the cubic continued fraction