So far we are applying a transform to two sequences interleaved appended by a constant \(C\), i.e \[T[C,s^{(1)},s^{(2)}]\] we can look at the relations between \(T[C,s^{(1)},s^{(2)}]\), \(T[C,s^{(1)},s^{(3)}]\) and \(T[C,s^{(1)},s^{(2)}+s^{(3)}]\) for various inputs. \[\begin{matrix} C & s^{(1)} & s^{(2)} & s^{(3)} & \frac{T[C,s^{(1)},s^{(2)}]+T[C,s^{(1)},s^{(3)}]}{T[C,s^{(1)},s^{(2)}+s^{(3)}]}\\ 1 & 1,2,3.. & 1,2,3... & 2,4,6... & \frac{2}{1}, \frac{2}{1}, \frac{5}{4}, \frac{19}{22}, \frac{99}{160}, \frac{661}{1456}\\ \end{matrix}\]
1,1,2,6,24,120,... 1,1,3,13,75,541,4683,... 1,1,4,22,160,1456,15904,...