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# Decagonal number

A decagonal number is a figurate number that represents a decagon. The decagonal number for n is given by the formula 4n2 - 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 nth heteromecic number, or to put it algebraically, Dn = n2 + 3(n2 - n).

Decagonal numbers consistently alternate parity.

03-10-2013 05:06:04