Centered dodecahedral number

Totalno. 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

Inmathematics, acentered dodecahedral number is acenteredfigurate number that represents adodecahedron. The centered dodecahedral number for a specificn is given by

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

The first such numbers are:1,33,155, 427, 909, 1661, 2743, 4215, 6137, 8569, … (sequenceA005904 in theOEIS).

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

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