pyramidal number

It is also the sum of the first five square pyramidal numbers.

The first terms of this series (the square pyramidal numbers) are:

Fourteen is the sum of the first three squares, which makes it a square pyramidal number.

The sum of two consecutive square pyramidal numbers is an octahedral number.

That is, the solution to the puzzle is given by the square pyramidal numbers.

Five is also a square pyramidal number.

A heptagonal pyramidal number is the sum of the first few heptagonal numbers.

Square pyramidal numbers are also related to tetrahedral numbers in a different way:

The number of squares in a square grid is similarly counted by the square pyramidal numbers.

The square pyramidal numbers can also be expressed as sums of binomial coefficients:

The term is most often used to refer to square pyramidal numbers, which have four sides, but it can also refer to:

The first few pentagonal pyramidal numbers are:

That is, centered hexagonal pyramidal numbers and cubes are the same numbers, but they represent different shapes.

A pyramidal number is a figurate number that represents a pyramid with a base and a given number of sides.

Therefore, the nth octahedral number can be obtained by adding two consecutive square pyramidal numbers together:

Square pyramidal number.

Square pyramidal numbers also solve the problem of counting the number of squares in an n x n grid.

Triangular pyramidal number (three sides)

Pentagonal pyramidal number (five sides)

Hexagonal pyramidal number (six sides)

Heptagonal pyramidal number (seven sides)

As a figurate number, 204 is a nonagonal number and a square pyramidal number (the sum of the first eight squares).

(the square pyramidal numbers)

The 'n'th pentagonal pyramidal number is also 'n' times the 'n'th triangular number.

Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number.