Decagonal number

A decagonal number is a figurate number that represents a decagon. The decagonal number for Failed to parse (Missing texvc executable; please see math/README to configure.): n

is given by the formula

Failed to parse (Missing texvc executable; please see math/README to configure.): 4n^2 - 3n

with Failed to parse (Missing texvc executable; please see math/README to configure.): 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 (sequence A001107 in OEIS)

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, Failed to parse (Missing texvc executable; please see math/README to configure.): D_n = n^2 + 3(n^2 - n) .

Decagonal numbers consistently alternate parity.