The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern sequences, which count the occurrences of a finite number of different patterns in the expansion of positive integers in any integer base, and analyze their partial sums.

翻译：自20世纪50年代以来，不同学者已对正整数二进制展开中特定模式出现次数的整数序列部分和进行了研究。本文引入广义模式序列，该序列统计正整数在任意整数基展开中有限个不同模式的出现次数，并分析其部分和性质。