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.