Vielen Dank Henrik for the tip and coding style suggestions, that was indeed the function I wanted:
Y1[n] = BooleanConvert[ If[If[Y[n - 2], If[Y[n - 3], a[n - 1], b[n - 1]], If[Y[n - 3], c[n - 1], d[n - 1]]], If[Y[n - 2], a[n], b[n]], If[Y[n - 2], c[n], d[n]]]] // TraditionalFormBooleanMinimize[Y21[n], "DNF"] // TraditionalForm
BooleanMinimize[Y1[n], "DNF"] // TraditionalFor
Collect[Y1[n], {Y[n - 1], ! Y[n - 1]}, Simplify] // TraditionalForm
Not yet in the simple sum of products I expected, but it is getting there.