If you take the Fibonacci sequence:
0, 1, 1, 2, 3...
and give them indexes like this:
0, 1, 2, 3, 4, 5...
0, 1, 1, 2, 3, 5...
you can double the index by taking any number in the series, for this example ill use 3.
If you add together the surrounding numbers then times it by the number you choose, it will double the index of your number, for example:
Number: 3
Surrounding numbers: 2 and 5
2+5=7, and 7x3=21.
If you continue the sequence, 21 is index 8.
0, 1, 2, 3, 4, 5, 6, 7, 8
0, 1, 1, 2, 3, 5, 8, 13,21
My question to you is there any other equations that does more than simply add or subtract one from the index of a number in the sequence, for example, is there one that always squares the index? Or even Factorial it?
