I have to calculate inverse Z transform by inversion integral method of

X(Z) = 1 / (1+ z^ -2) (z raise to power -2)

I have done it in matlab and by computation menthod and answer comes to be same as

[1 0 -1 0 1 0 -1 - - - - - ]

but when i do it with inversion integral my answer comes to be i^k ( i= iota)

if i put values of k as 0 1 2 3 my answers does not match

plz help me