Dodecagonal number

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A dodecagonal number is a figurate number that represents a dodecagon. The dodecagonal number for n is given by the formula

5n^2 - 4n; n > 0

The first few dodecagonal numbers are:

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 OEIS)

The dodecagonal number for n can also be calculated by adding the square of n to four times the (n - 1)th pronic number, or to put it algebraically, D_n = n^2 + 4(n^2 - n).

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.

By the Fermat polygonal number theorem, every number is the sum of at most 12 dodecagonal numbers.

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