- Source: 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
(
2
n
+
1
)
(
5
n
2
+
5
n
+
1
)
{\displaystyle (2n+1)\left(5n^{2}+5n+1\right)}
The first such numbers are: 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, … (sequence A005904 in the OEIS).
Congruence Relations
C
D
C
(
n
)
≡
1
(
mod
2
)
{\displaystyle CDC(n)\equiv 1{\pmod {2}}}
C
D
C
(
n
)
≡
1
−
n
(
mod
3
)
{\displaystyle CDC(n)\equiv 1-n{\pmod {3}}}
C
D
C
(
n
)
≡
2
n
+
1
(
mod
3
,
5
,
6
,
10
)
{\displaystyle CDC(n)\equiv 2n+1{\pmod {3,5,6,10}}}