Try this. It shows an example with symbolic variables to show that it creates the correct matrix. You can try it with k as a numeric vector
k = sym('k', [1, 8]);
A = diag(k(2:end-1),1) + diag(k(2:end-1),-1) + diag(k(1:end-1)+k(2:end));
Result
>> A
A =
[ k1 + k2, k2, 0, 0, 0, 0, 0]
[ k2, k2 + k3, k3, 0, 0, 0, 0]
[ 0, k3, k3 + k4, k4, 0, 0, 0]
[ 0, 0, k4, k4 + k5, k5, 0, 0]
[ 0, 0, 0, k5, k5 + k6, k6, 0]
[ 0, 0, 0, 0, k6, k6 + k7, k7]
[ 0, 0, 0, 0, 0, k7, k7 + k8]
