Dodecagonal number
A dodecagonal number is a figurate number that represents a dodecagon. The dodecagonal number for n is given by the formula
![{\displaystyle D_{n}=5n^{2}-4n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/754a25bf1b2310d26330b0b3411dacd367820e19)
The first few dodecagonal numbers are:
- 0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652, 9073, 9504, 9945 ... (sequence A051624 in the OEIS)
Properties
- The dodecagonal number for n can be calculated by adding the square of n to four times the (n - 1)th pronic number, or to put it algebraically,
.
- Dodecagonal numbers consistently alternate parity, and in base 10, their units place digits follow the pattern 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.
is the sum of the first n natural numbers congruent to 1 mod 10.
is the sum of all odd numbers from 4n+1 to 6n+1.
See also
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| | | | Possessing a specific set of other numbers |
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| Expressible via specific sums |
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