Tree Planting Problems

How many rows of k trees can you make by planting n trees? Here are the best known bounds for small values of k and n. Click on the links for pictures.

Maximum Number of Rows of k using n trees
k \ n 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
3 1 1 2 4 6 7 10 12 16 19 22-24 26-27 31-32 37 40-42 46-48 52-54 57-60 64-67 70-73 77-81 85-88 92-96
4 0 1 1 1 2 2 3 5 6 7 9 10 12 15 16 18 20-28 23-30 24-31 26-38 28-40 30-42 32-50
5 0 0 1 1 1 1 2 2 2 3 3 4 6-9 6-9 7-13 9-14 10-15 11-16 12-18
6 0 0 0 1 1 1 1 1 2 2 2 2 3 3 3 4 4 5 7

More information can be found at MathWorld.

This problem restricted to the integer lattice can be found at Infinite Search Space.

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