How many distinct distributions (x,y,z,w) of n
identical marbles in 4 boxes labeled A,B,C and D are there, such that
x,y,z,w are positive integers in strictly increasing order?
Verify the validity of your formula (or set of formulas) by manual listing of all such distributions for n=18.
(In reply to re: solution - OEIS
by Brian Smith)
The n+10 is an obvious start and could be dispensed with immediately if the problem is reworded to non-negative integers and non-decreasing order. I solved the problem for 2 boxes and almost for 3. The recursive structure is apparent.
If to build up marble by marble you can keep the piles from growing too fast by reducing x to zero every time it goes to 1. 1,y,z,w -> 0,y-1,z-1,w-1. This allows you to have only three variables to keep track of. It also makes the recursive stucture more apparent. I didn't go far enough to see it going back nine terms though!
Posted by Jer
on 2017-08-17 15:20:50