In this paper, we examine the two issues of mining association rules and mining sequential patterns in a large database of sales transactions. The problems of mining association rules and mining sequential patterns focus on discovering large itemsets and large sequences, respectively. We present PSI and PSI.seq for efficient large itemsets generation and large sequences generation, respectively. The main ideas of these two algorithms are using prestored information to minimize the numbers of candidate itemsets and candidate sequences counted in each database scan. The prestored informations for PSI and PSI.seq include the itemsets and the sequences along with their support counts found in the last mining, respectively. Typically a user may require to tune the value of the minimum support many times before a set of useful association rules can be obtained from the transaction database. Using prestored information, the total computation time will be reduced effectively. Empirical results how that our approaches outperform previous methods by an order of magnitude, using little storage space for the prestored information.