A general relation between sums of cubes and triangular pyramidal numbers - Mohamat Johari, Mohamat Aidil; Mohd Atan, Kamel Ariffin; Sapar, Siti Hasana (American Institute of Physics, 2011)
Let ck(m) denote the number of representations of integer m as a sum of k cubes and pk(m) denote the number of representations of integer m as a sum of k triangular pyramidal numbers. We give a relation pk(m) = coddk (ν) where ν = 48m – 24n+2ñ+k and coddk (ν) denotes the number of representations of integer ν as a sum of k odd cubes, for a single value of m. A general relation between number of representations between Σki=1 xsi and its associated polytopic numbers for any orders of s, is also given.