What is pyramidal number sequence?

Answer 1

It is a sequence in which the numbers represent the number of spheres in a pyramidal stack of spheres. There are a number of possible configurations for stacking spheres - a visit to fruit stalls may show you options.

The square based pyramidal numbers are given by the sums of the first n square numbers. So

U(1) = 1^1 = 1

U(2) = 1^2 + 2^2 = 1 + 4 = 5

and so on

U(n) = 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6.

However, there are also triangle based pyramidal numbers and hexagon based pyramidal numbers, since these configuration also give stable stacks.

Answer 2

Pyramid number is a migrate number corresponding to a configuration of points which form a pyramid with -sided regular polygon bases can be thought of as a generalized pyramidal number, and has the form Pnr = n(n+1)(n(r-2) + 5 - r)/6

For example: Pn3 =n (n+1)(n+2)/6