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

${\displaystyle (2n+1)\left(5n^{2}+5n+1\right)}$

Centered dodecahedral number

Total no. of terms	Infinity
Subsequence of	Polyhedral numbers
Formula	${\displaystyle (2n+1)\,(5n^{2}+5n+1)}$
First terms	1, 33, 155, 427, 909, 1661
OEIS index	A005904 Centered dodecahedral

The first such numbers are: 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, … (sequence A005904 in the OEIS).

Congruence Relations

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