How to find a number of solutions for $x_1+x_2+\ldots+x_n=r$ where $r$ is divisible by 3 and for a given $l$ and $r$ such that $l\leq x_i \leq r$?

Asked Jan 20 '19 at 13:58

Active Jan 21 '19 at 11:17

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How to find a number of solutions for $x_1+x_2+\ldots+x_n=r$ where $r$ is divisible by 3 and for a given $l$ and $r$ such that $l\leq x_i \leq r$?

edited Jan 21 '19 at 11:17

N. F. Taussig

asked Jan 20 '19 at 13:58

Sail Akhil

1

what is this have to do with Taylor expansion? – tortue Jan 20 '19 at 14:02
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Letting $y_i=x_i-l$ this becomes a routine Stars and Bars problem. $r$ can be whatever you want...divisibility by $3$ doesn't change the computation. – lulu Jan 20 '19 at 14:10
Or maybe using generating functions, similar to this. – rtybase Jan 21 '19 at 12:52

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