Worth noting that, a pulse should be defined as 1/4 up, 1/2 down, 1/4 up. Not 1/2 up, 1/2 down.
Is it worth noting that the two sequences are the same?
"1/4 up, 1/2 down, 1/4 up" + "1/4 up, 1/2 down, 1/4 up" + "1/4 up, 1/2 down, 1/4 up" + ...
= "1/4 up, " + "1/2 down, 1/4 up + 1/4 up" + "1/2 down, 1/4 up + 1/4up" + "1/2 down, 1/4 up + 1/4up" + ...
= "1/4 up, " + "1/2 down, 1/2 up" + "1/2 down, 1/2 up" + "1/2 down, 1/2 up" + ...
Also, for what the OP is trying to do, a half bridge would work.