That's such a cool idea. Do you then prove it is the formula you need, or do you just assume that if it matches for 10 terms it's probably the formula?
A math professor I had in college, Dave Kelly, had a trick where he'd show a seemingly reasonably-behaved sequence, explain where it came from, then show that the rest of the sequence was absurd -- like, it would be exponential for a while and then zero, or increase arithmetically for a while and then become undefined, etc. I wish I had taped that.
Rarely have I found it to be that easy. Generally you'll get a hit on a partial match of your sequence but from that you'll learn about some number theory regarding that sequence or there will be links, formulas and code snippets that help you further research your specific algorithm you're trying to solve. You're just looking for that 'aha!' moment and this database usually delivers. Sometimes that 'aha' is the realization that it's going to be impossible or take too much time or resources to compute and that's just as helpful.
Recursive/fractal sequences are toughest because there's very likely no direct computation. Say your sequence matches with a fractal sequence at only every fifth element, you still have to compute the elements you don't need to get the ones you do need. Sometimes you need a number theory math library to do the computation and that kind of dependency is overkill so now you've got to figure out how recreate just the parts of that math library you need or discover a shortcut (again, using the sequence database.) Invariably you'll discover something new and be able to contribute back.
Ditto, especially with certain programming interview problems or Advent of Code, etc.
You build the small-N brute forcing demo, and then the integer sequences (from correct answers, or from how the overall number of solutions grows) may help find the formal math jargon name behind whatever's going on.
For example, Stirling Numbers of the First Kind [0].
That's such a cool idea. Do you then prove it is the formula you need, or do you just assume that if it matches for 10 terms it's probably the formula?
A math professor I had in college, Dave Kelly, had a trick where he'd show a seemingly reasonably-behaved sequence, explain where it came from, then show that the rest of the sequence was absurd -- like, it would be exponential for a while and then zero, or increase arithmetically for a while and then become undefined, etc. I wish I had taped that.
Rarely have I found it to be that easy. Generally you'll get a hit on a partial match of your sequence but from that you'll learn about some number theory regarding that sequence or there will be links, formulas and code snippets that help you further research your specific algorithm you're trying to solve. You're just looking for that 'aha!' moment and this database usually delivers. Sometimes that 'aha' is the realization that it's going to be impossible or take too much time or resources to compute and that's just as helpful.
Recursive/fractal sequences are toughest because there's very likely no direct computation. Say your sequence matches with a fractal sequence at only every fifth element, you still have to compute the elements you don't need to get the ones you do need. Sometimes you need a number theory math library to do the computation and that kind of dependency is overkill so now you've got to figure out how recreate just the parts of that math library you need or discover a shortcut (again, using the sequence database.) Invariably you'll discover something new and be able to contribute back.
Ditto, especially with certain programming interview problems or Advent of Code, etc.
You build the small-N brute forcing demo, and then the integer sequences (from correct answers, or from how the overall number of solutions grows) may help find the formal math jargon name behind whatever's going on.
For example, Stirling Numbers of the First Kind [0].
[0] https://en.m.wikipedia.org/wiki/Stirling_numbers_of_the_firs...