Centered Hexagonal Number

A centered hexagonal number is a figurate number formed by a hexagonal arrangement of dots with one dot at the center and every other dot surrounding it in successive hexagonal rings, giving the sequence 1, 7, 19, 37, 61, 91 and so on. The nth centered hexagonal number is given by the formula 3n squared minus 3n plus 1, which is equal to n cubed minus (n minus 1) cubed, showing that each centered hexagonal number is the difference between two consecutive perfect cubes. It can also be written as 1 plus six times the (n minus 1)th triangular number, linking the sequence to the triangular numbers, and whether a given number H is a centered hexagonal number can be tested by checking whether (3 plus the square root of (12H minus 3)) divided by 6 comes out to a whole number.