南通职业大学学报2025，Vol.39Issue(4)：53-56,4.DOI:10.3969/j.issn.1008-5327.2025.04.010
正整数分解成四个三角形数线性组合的方法数的精确表达式B(1,1,3,9;a)
An Exact Formula for the Number of Ways to Express a Positive Integer as a Linear Combination of Four Triangular Numbers:B(1,1,3,9;a)
摘要
Abstract
Based on the identities and properties of Ramanujan theta functions ψ(q)and ψ(q),for four asymmetric coefficients(1,1,3,9),the relationship between the number of representations of a positive integer as a linear combination of four square numbers and that as a linear combination of four triangular numbers is established.Then an exact formula for the number of representations of a positive integer as a linear combination of four triangular numbers with asymmetric coefficients B(1,1,3,9;a)is obtained.关键词
四个三角形数/theta函数/表示方法数/非对称系数/B(1,1,3,9/a)Key words
four triangular numbers/theta function/number of representations/asymmetric coefficient/B(1,1,3,9/a)分类
数理科学引用本文复制引用
王敏,程德胜..正整数分解成四个三角形数线性组合的方法数的精确表达式B(1,1,3,9;a)[J].南通职业大学学报,2025,39(4):53-56,4.基金项目
江苏省高校哲学社会科学研究一般项目(2024SJYB0507) （2024SJYB0507）
江苏联合职业技术学院课题(B/2024/7/008) （B/2024/7/008）
南京高等职业技术学校课题(2024L-008) （2024L-008）
