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Decagonal Number
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Wikipedia
A decagonal number is a figurate number that represents a decagon. The decagonal number for n is given by the formula

4n^2 - 3n

with n > 0. The first few decagonal numbers are

1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326, 8695, 9072, 9457, 9850

The decagonal number for n can also be calculated by adding the square of n to thrice the (n - 1)th pronic number, or to put it algebraically, D_n = n^2 + 3(n^2 - n).

Decagonal numbers consistently alternate parity.

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Last updated on Wednesday December 27, 2006 at 04:20:12 PST (GMT -0800)
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