Centered Hexagonal Number as Sum of Triangular Numbers/Visual Demonstration

Theorem

Let $C_n$ be the $n$th centered hexagonal number.

Then:

$C_n = 6 T_{n - 1} + 1$

where $T_{n - 1}$ denotes the $n - 1$th triangular number.

Visual Demonstration

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $37$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $37$