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 Marbles in boxes (Posted on 2017-08-16)
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.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re(2): solution - OEIS Comment 5 of 5 |
(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
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