Return to Answer

f1 = FoldList[Plus, #, 3 Mod[Range[0, 2 (# - 2)], 2] - 2] &

f1 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f1 @ 4

{4, 2, 3, 1, 2, 0}

Also

f2 = Accumulate[Prepend[#]@{-2, 1}(3 Mod[Range[0, 2 (# - 2)], 2] - 2) &;

f2 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f2  @ 4

{4, 2, 3, 1, 2, 0}

f1 = FoldList[Plus, #, 3 Mod[Range[0, 2 (# - 2)], 2] - 2] &

f1 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f1 @ 4

{4, 2, 3, 1, 2, 0}

Also

f2 = Accumulate @ Prepend[#] @ (3 Mod[Range[0, 2 (# - 2)], 2] - 2) &;

f2 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f2  @ 4

{4, 2, 3, 1, 2, 0}

f1 = FoldList[Plus, #, {-2, 1}[[Mod[Range[2 # - 3], 2, 1]]]] &

f1 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f1 @ 4

{4, 2, 3, 1, 2, 0}

Also

f2 = Accumulate[Prepend[#]@{-2, 1}[[Mod[Range[2  # - 3], 2, 1]]]] &;

f2 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f2  @ 4

{4, 2, 3, 1, 2, 0}

f1 = FoldList[Plus, #, 3 Mod[Range[0, 2 (# - 2)], 2] - 2] &

f1 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f1 @ 4

{4, 2, 3, 1, 2, 0}

Also

f2 = Accumulate[Prepend[#]@{-2, 1}(3 Mod[Range[0, 2 (# - 2)], 2] - 2) &;

f2 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f2  @ 4

{4, 2, 3, 1, 2, 0}

f = FoldList[Plus, #, {-2, 1}[[Mod[Range[2 # - 3], 2, 1]]]] &

f @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f @ 4

{4, 2, 3, 1, 2, 0}

f1 = FoldList[Plus, #, {-2, 1}[[Mod[Range[2 # - 3], 2, 1]]]] &

f1 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f1 @ 4

{4, 2, 3, 1, 2, 0}

Also

f2 = Accumulate[Prepend[#]@{-2, 1}[[Mod[Range[2  # - 3], 2, 1]]]] &;

f2 @ 5

{5, 3, 4, 2, 3, 1, 2, 0}

f2  @ 4

{4, 2, 3, 1, 2, 0}