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AN INTEGER SEQUENCE WHICH IS THE SUM OF TRIANGULAR NUMBERS AND EXTRA NUMBERS
Keywords:
integer sequence, triangular numberDOI:
https://doi.org/10.17654/0972555525030Abstract
We fix a positive integer $n$. For each positive integer $k$, we define $X(n, k)$ to be set consisting of the pair of integers $(a, b)$ which satisfies $a^2+b^2=k$ and $1 \leq a<b \leq n$. Let $|X(n, k)|$ be the cardinality of $X(n, k)$ and we define $P(n)$ to be the sum of $|X(n, k)|^2$ over $k$. In this paper, we study the properties of the integer sequence $P(n)$.
Received: May 29, 2025
Accepted: July 28, 2025
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