You have N sticks with lengths 1, 2, 3, ..., N.
Provide a closed form function in terms of N for the number of distinct valid triangles can you make from these N sticks.
note: reflections and rotations are considered to be the same, and valid triangles must have positive area.
Inspired by 5, 6, Pick Up Sticks
(In reply to
computer solution by Charlie)
Another formula (for alternating signs) under A002623 looks a bit simpler than the modified Jerry W. Lewis formula.
Adjusted to make it not alternate signs, for offset and simplified, it's:
5*N / 12 - 3*N^2 / 8 + N^3 / 12 - 1/16 + (-1)^N / 16
Edited on May 27, 2025, 10:30 am
|
|
Posted by Charlie
on 2025-05-27 10:29:01 |
re: computer solution
