Linear Convolution without using conv(A, B)

It is a basic operation to calculate the output for any linear time invariant system given its input and its impulse response.

Enter x
[1 2 3 4 5]
Enter the lower limit:
-1
Enter the upper limit:
3
Enter h:
[1 2 3]
Enter the lower limit:
-2
Enter the upper limit:
0
x(n) is:
1 2 3 4 5

h(n) is:
1 2 3

y(n) is:
1 4 10 16 22 22 15