Decagonal number
Encyclopedia : D : DE : DEC : 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 (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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