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Nonagonal Number




{7n^2 - 5n}\over 2

The first few nonagonal numbers are:

: 1 , 9 , 24 , 46 , 75 , 111 , 154 , 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089 , 1216, 1350, 1491, 1639, 1794, 1956, 2125, 2301, 2484, 2674, 2871, 3075, 3286, 3504, 3729, 3961, 4200, 4446, 4699, 4959, 5226, 5500, 5781, 6069, 6364, 6666, 6975, 7291, 7614, 7944, 8281, 8625, 8976, 9334, 9699.

The Parity of nonagonal numbers follows the pattern odd-odd-even-even.

A nonagonal number times 7, plus 3 is equal to a Triangular Number . In particular, if ''N(n)'' represents the ''n''th nonagonal number, and ''T(n)'' represents the ''n''th triangular number, then {7N(n) + 3 = T(7n - 3)}