How many ways can three numbers add up to eleven?

10 ways
{9, 1, 1}, {8, 2, 1}, {7, 3, 1}, {7, 2, 2}, {6, 4, 1},
{6, 3, 2}, {5, 5, 1}, {5, 4, 2}, {5, 3, 3}, {4, 4, 3}

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Perhaps if you examine these, you can see the pattern.

For each integer in the range 3 to 20, the number of 3-way partitions is indicated here.
{3, 1}, {4, 1}, {5, 2}, {6, 3}, {7, 4}, {8, 5}, {9, 7}, {10, 8},
{11, 10}, {12, 12}, {13, 14}, {14, 16}, {15, 19}, {16, 21}, {17, 24},
{18, 27}, {19, 30}, {20, 33}