Reduce[] giving incorrect result for equation over $\mathbb{Z}^4$

Question

This is partially in response to a question I posted earlier, although the problem in this case appears to be distinct from the problem there, so I am temporarily filing this as a separate question.

Executing

Length[Reduce[Abs[c1] + Abs[c2] + Abs[c3] + Abs[c4] <= 19, {c1, c2, c3, c4}, Integers]]

yields 97281, which is in full agreement with the result obtained when Reduce is replaced by Solve.

However, executing

Length[Reduce[Abs[c1] + Abs[c2] + Abs[c3] + Abs[c4] <= 22, {c1, c2, c3, c4}, Integers]]

yields 42736. This is obviously impossible, since the number of $\mathbb{Z}^4$ lattice points within a taxicab ball is a strictly increasing function of radius.

Does anyone know what is going wrong here? I am going to temporarily solve the problem via alternate, more delicate approaches seeing as both Solve[] and Reduce[] have failed to give correct answers for $r\geq20$, but any insight as to this sudden behavioral discontinuity would be appreciated.

EDIT: It may be possible that the lower than expected result from Length may be due to Reduce outputting a solution set whose expression depth was not just that of the simple Or[...] structure that it normally gives for smaller values of $r$. If anyone can confirm this, I'll close this question.

Answer 1

If you try:

ListLinePlot[{#, Length@Reduce[Abs[c1] + Abs[c2] + Abs[c3] + Abs[c4] <= # && 
                 And @@ Thread[{c1, c2, c3, c4} >= 0], {c1, c2, c3, c4}, Integers]} & /@ 
                                                                            Range[2, 20]]

You'll get:

It only means that Reduce[] is expressing its results in a different way. Take a look at them and then post your own answer :)