Mathematical analysis derives a test criterion for tetrahedral numbers, providing an efficient method to verify figurate integer sequences.
The nth triangular number is defined by tn=1+2+3+⋯+n, while the nth tetrahedral number is defined by Tn=t1+t2+t3+⋯+tn. It can easily be shown [1] that tn=n(n+1)2andTn=n(n+1)(n+2)6. There is a ve...
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Subramaniam et al. (2026) studied this question.
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