But I just reworked my code to check for differences between successive terms only requiring that they be equal (whether pos or neg).  Looking just at complete sequences of 7 terms.

The only solution was the increasing one everyone has found.

However, in my original interpretation 3 solutions had two groups, the "N" group and the "T" group:  in any of those, either one or both of the groups could be reversed, wlog, and decreasing short sequences of 3 or 4 terms can be obtained.