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[IcyTea31]

[10, 5, 10, 15, 10, 20, 10, 5]
[4, 3, 4, 3]
[4, 1, 4, 1]
?

Yes to all.

[Naturegirl1999]

Spoiler: Valid Patterns (click to show/hide)

[5,4,5,6,5,7,5,4]
[10,5,10,15]
[10, 5, 10, 15, 10, 20, 10, 5]
[4, 3, 4, 3]
[4, 1, 4, 1]
[4,1,4,3]

Spoiler: Invalid Patterns (click to show/hide)

[5, 1, 5, 1, 5, 1, 5, 1]
[a, b, a, c1, a, c2, ...]
[5,5]
[5,6]
[5,7,5,6]
[5,9,5,9]

Is the pattern x+n-n+(n(+/-b)) where b decreases/increases by the same amount each cycle

[IcyTea31]

Is the pattern x+n-n+(n(+/-b)) where b decreases/increases by the same amount each cycle

I don't understand that function perfectly, but I think no, because [1,0,4,7] fits the pattern. What does x stand for, and what do you mean by cycle?

[Naturegirl1999]

x is the initial number, and a cycle is when it goes back to the number it started with

[IcyTea31]

In that case no, because [4,1,4,2,4,3] does not fit the pattern.