A general relation between sums of cubes and triangular pyramidal numbers

Johari, M. A. M.; Atan, K. A. M.; Sapar, S. H.
May 2012
AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p275
Academic Journal
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.


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