Two Simple Ways of Generating the Partitions of (n+1) from the Partitions of n

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I propose two simple ways of generating the partitions of (n+1) from the partitions of n. A recurrence relation for P(n+1), the number of partitions of (n+1), in terms of P(n) and Q(n), where Q(n) denotes the number of partitions of n having strictly different last two parts is obtained. Also a generating function for Q(n) is given. The other method for generating the partitions of (n+1) from the partitions of n is discussed at the end.