Centered dodecahedral number

In mathematics, a centered dodecahedral number is a centered figurate number that represents a dodecahedron. The centered dodecahedral number for a specific n is given by

$(2n+1)(5n^2+5n+1)$

The first such numbers are: 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, … Template:OEIS.

Congruence Relations

• $CDC(n)\equiv 1(\mathrm{mod}2)$
• $CDC(n)\equiv 1-n(\mathrm{mod}3)$
• $CDC(n)\equiv 2n+1(\mathrm{mod}3,5,6,10)$