Tetrahedral Number Calculator
Enter a term index n to compute the n-th tetrahedral number n(n+1)(n+2)/6. Shows the matching triangular number, the first term, and a table of the sequence.
Input
Enter a positive integer n to compute the n-th tetrahedral (triangular pyramidal) number.
Integer of 1 or more
Result
The 5-th tetrahedral number
35
Matching triangular number T(n)
15
First term Te(1)
1
A tetrahedral number stacks triangular numbers: Te(n) = n(n+1)(n+2)/6 = T(1) + T(2) + ... + T(n), where T(k) = k(k+1)/2.
Sequence table
| Index k | Triangular T(k) | Tetrahedral Te(k) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 3 | 4 |
| 3 | 6 | 10 |
| 4 | 10 | 20 |
| 5 | 15 | 35 |
How it works
- The n-th tetrahedral number is Te(n) = n(n+1)(n+2)/6.
- A tetrahedral number is the sum of triangular numbers stacked from the top: Te(n) = T(1) + T(2) + ... + T(n).
- Here the k-th triangular number is T(k) = k(k+1)/2.
- For n equal to 1, 2, 3, 4, 5 the tetrahedral numbers are 1, 4, 10, 20, 35.
- Only positive integers are accepted. The sequence table shows up to the first 20 terms.
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Tetrahedral Number Calculator