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 nonnegative integers and nondecreasing 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,y1,z1,w1. 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 20170817 15:20:50 