Definitions

nonagonal

Nonagonal number

A nonagonal number or enneagonal number is a figurate number that represents a nonagon. The nonagonal number for n is given by the formula:

frac {7n^2 - 5n}{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.

Letting N(n) give the nth nonagonal number and T(n) the nth triangular number,

{7N(n) + 3 = T(7n - 3)}.

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