In the Fibonacci sequence, each number is the sum of the two preceding ones:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, …
This produces two notable secondary patterns: Summing the squares of each pair of adjacent entries yields an even-numbered term in the sequence:
12 + 12 = 2
12 + 22 = 5
22 + 32 = 13
32 + 52 = 34
52 + 82 = 89
82 + 132 = 233
132 + 212 = 610
And the odd-numbered terms between these are the differences of squares of terms taken two by two, two places apart:
22 – 12 = 3
32 – 12 = 8
52 – 22 = 21
82 – 32 = 55
132 – 52 = 144
212 – 82 = 377
342 – 132 = 987
… and so on.