Tetrahedral Number as Sum of Squares/Examples
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Examples of Tetrahedral Number as Sum of Squares
Let $H_n$ denote the $n$th tetrahedral number.
Then:
\(\ds H_1\) | \(=\) | \(\, \ds 1 \, \) | \(\, \ds = \, \) | \(\ds 1^2\) | ||||||||||
\(\ds H_2\) | \(=\) | \(\, \ds 4 \, \) | \(\, \ds = \, \) | \(\ds 2^2\) | ||||||||||
\(\ds H_3\) | \(=\) | \(\, \ds 10 \, \) | \(\, \ds = \, \) | \(\ds 1^2 + 3^2\) | ||||||||||
\(\ds H_4\) | \(=\) | \(\, \ds 20 \, \) | \(\, \ds = \, \) | \(\ds 2^2 + 4^2\) | ||||||||||
\(\ds H_5\) | \(=\) | \(\, \ds 35 \, \) | \(\, \ds = \, \) | \(\ds 1^2 + 3^2 + 5^2\) | ||||||||||
\(\ds H_6\) | \(=\) | \(\, \ds 56 \, \) | \(\, \ds = \, \) | \(\ds 2^2 + 4^2 + 6^2\) | ||||||||||
\(\ds H_7\) | \(=\) | \(\, \ds 84 \, \) | \(\, \ds = \, \) | \(\ds 1^2 + 3^2 + 5^2 + 7^2\) |
... and so on.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $56$