Tetrahedral Number Sequence
This is the Tetrahedral Number Sequence:
1, 4, 10, 20, 35, ...
We can understand it better when we think of a stack of marbles in the shape of a Tetrahedron.
Just count how many marbles are needed for a stack of a certain height.
- For height=1 we only need 1 marble
- For height=2, we need 4 marbles (1 at the top and 3 below)
- For height=3 we need 10 marbles.
- For height=4 we need 20 marbles.
- For height=5 we need 35 marbles.
- How many for height=6 ... ?
Triangular and Tetrahedral Numbers
This table shows the values for the first few layers:
|n||Triangular Number||Tetrahedral Number|
|(Height)||(Marbles in Layer)||(Total Marbles)|
Looking at the numbers we see something interesting: when we take any number and add the number before it and to the left we get the next number in the sequence. (For example 4+6=10).