# Sums of triangular numbers and sums of squares

@inproceedings{Akbary2021SumsOT, title={Sums of triangular numbers and sums of squares}, author={Amir Akbary and Zafer Selcuk Aygin}, year={2021} }

For non-negative integers a, b, and n, let Npa, b;nq be the number of representations of n as a sum of squares with coefficients 1 or 3 (a of ones and b of threes). Let Npa, b;nq be the number of representations of n as a sum of odd squares with coefficients 1 or 3 (a of ones and b of threes). We have that Npa, b; 8n ` a ` 3bq is the number of representations of n as a sum of triangular numbers with coefficients 1 or 3 (a of ones and b of threes). It is known that for a and b satisfying 1 ď a…

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