Centered dodecahedral numberTotal no. of terms | Infinity |
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Subsequence of | Polyhedral numbers |
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Formula | ![{\displaystyle (2n+1)\,(5n^{2}+5n+1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/83539456f3340a6a19ab3699af9fee9f33a63036) |
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First terms | 1, 33, 155, 427, 909, 1661 |
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OEIS index | - A005904
- Centered dodecahedral
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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)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d915801946ed93a4cdcbb3d285e2ae79d2bcf355)
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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e5366b006103d189b7aaa4f3650cbc96a981c39)
![{\displaystyle CDC(n)\equiv 1-n{\pmod {3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b878a032bfe92f061087b816901586961fb18ee6)
![{\displaystyle CDC(n)\equiv 2n+1{\pmod {3,5,6,10}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e37b4bbaeb83795ab3a8ef9b0e74a5762b8330ff)
Figurate numbers
2-dimensional | centered | - Centered triangular numbers
- Centered square numbers
- Centered pentagonal numbers
- Centered hexagonal numbers
- Centered heptagonal numbers
- Centered octagonal numbers
- Centered nonagonal numbers
- Centered decagonal numbers
- Star numbers
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Possessing a specific set of other numbers |
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Expressible via specific sums |
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Mathematics portal |
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