Central polygonal numbers

Rule

Each term is: Multiply by the next smaller number, divide by two, and add one

Known as: Central polygonal numbers

Central polygonal numbers

The maximum number of pieces of a circular pizza you can make with n straight slices.

The first 50 terms (starting from n=1) are:

1 2 4 7 11 16 22 29 37 46 56 67 79 92 106 121 137 154 172 191 211 232 254 277 301 326 352 379 407 436 466 497 529 562 596 631 667 704 742 781 821 862 904 947 991 1036 1082 1129 1177 1226

Example

To get the value for n=13:

  • Multiply by the next smaller number, giving 156.
  • Divide by two, giving 78.
  • Add one, giving 79.

So the result is 79.

References

On-Line Encyclopedia of Integer Sequences