The simplest way that I came up with is to initialize the first 2 ints in the array to 1, and then run a loop from 2 to the number of numbers you want to put in the sequence. In each iteration, assign num[count] to the sum of num[count-2] and num[count-1], like so...
Comments
num[0] = 1;
num[1] = 1;
for (count = 2; count < 10; count++)
num[count] = num[count-2] + num[count-2];