This one might be new to you.

The Serious bit.
This is from a branch of recreational mathematics called Figurate Numbers

The subtlety is this. For every convex polygon there are two figurate numbers.

For every convex polyhedron there are three figurate numbers.

The numbers 1, 5, 13, 25, 41, … are called A001844 in the OEIS (Online encyclopaedia of integer sequences) and are called the centred square numbers.

In 3-D, the three types of cubic numbers will be familiar to everybody. They are

• The simple cubic numbers 1, 8, 27, 64, 125, … A000578
• The body-centred cubic numbers 1, 9, 33, …
• The face-centred cubic numbers 1, 13, …

.thankS

Calculated the bcc & fcc numbers.

In 3-D, the three types of cubic numbers will be familiar to everybody. They are

• The simple cubic numbers 1, 8, 27, 64, 125, … A000578
• The body-centred cubic numbers 1, 9, 35, 91, 189, 341, 559, … A005898
• The face-centred cubic numbers 1, 14, 63, 172, 365, 666, 1099, … A050492

I’d miscalculated earlier.