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Compute constrained summation?

Posted 9 years ago

Screenshot.

P0, P1 and P2 are constants. The problem is to assign a,b,c all possible values so that their sum is always 33 and compute the sum.

4 Replies

I suggest you start by trying to implement a simpler problem of the same type.

POSTED BY: Frank Kampas
Sum[33! p0^a p1^b p2^c Boole[a + b + c == 33]/(a! b! c!), {a, 0, 33}, {b, 0, 33}, {c, 0, 33}]

huge output

POSTED BY: S M Blinder

Do you mean also $b\ge0$ and $c\ge0$? Else, for each $a$ there are an infinite number of integer pairs $a,b$. Otherwise you could generate an index set with:

t = Flatten[Table[{i, j, k}, {i, 0, 33}, {j, 0, 33}, {k, 0, 33}], 2];
indx=Select[t, (Total[#] === 33) \[And] (#[[2]] + #[[3]] > 0) &];
POSTED BY: John McGee
Posted 9 years ago

IntegerPartitions might be useful, but that uses positive values and needs a tweak to also include a=0

Join[Map[Join[{0}, #]&, IntegerPartitions[33, {2}]], IntegerPartitions[33, {3}]]
POSTED BY: Bill Simpson
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