From Wikipedia, the free encyclopedia
A dodecagonal number is a
figurate number that represents a
dodecagon. The dodecagonal number for n is given by the formula
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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