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Comment by segfaultbuserr | Hacker News Reader

OEIS solves real-world problems! One time I needed to optimize accesses to a data structure in my code. By trying out a few examples, I found the optimal order of iterations followed a particular number sequence, but I had no idea on how it could be deduced or calculated analytically. I entered the few examples I had into OEIS and found the solution. The solution involves graduate-level combinatorics and there was no way that I could solve it.

Thanks Neil Sloane and OEIS.

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I suspect this happens more often than anyone realizes.

I really want to read or write the sci-fi story where aliens ping our intelligence with some obscure sequence and they think we're geniuses because thanks to the OEIS we're all like "Oh, yeah, that's just A260151, numerators of coefficients c(n) in asymptotic expansion of Sum_{m=1..k} sqrt(m) ~ zeta(-1/2) + (2/3)*k^(3/2) + (-1/2)*k^(1/2) + Sum_{n=0..inf} c(n)/k^(2*n+1/2)., here's the next 50 terms" https://oeis.org/A260151 in about two minutes.

I had a very similar experience—discovering Stirling numbers of the second kind by solving a computer science problem through brute force, then plugging the results into OEIS, then reverse-engineering an elegant solution to the problem. Fantastic resource.

This sounds fascinating! What was the structure, and what was the sequence?

I can't give any detail, but the solution to my problem involves k-variate k-nomial multinomial coefficients [1]. It's a generalization of the binomial coefficients to high-order scenarios such as trinomial coefficients, quadrinomial coefficients, etc. In other words, from a Pascal triangle to a Pascal pyramid, to a Pascal hyperpyramid.

[1] https://oeis.org/wiki/Multinomial_coefficients

Multinomial coefficients are also used to define the multinomial distribution in probability which models e.g. the problem of "if I throw a fair die n times, how likely is it that I get exactly x1 ones, x2 twos, ..., x6 sixes?" - which is a generalisation of the binomial distribution in which there are only two cases.

This is not "graduate-level", it's a straightforward generalization of something that all school age kids learn. (Which is not too say that it's trivial to obtain an expression. I'm just saying it's not conceptually advanced)

Per a nitty exploitable quote, do you have the slightest idea how little that narrows it down?

You can generalize addition to semigroups but that's not a point, eh?

That's like arguing all math is addition (it's just a bunch of sum signs), therefore all math is not actually graduate level. It's a straightforward generalization of something that all school kids learn.

Also, math achievement in America is horrible. 40% of students leave 12th grade at "Less than Basic". Only 2-3% leave 12th grade at "Advanced." Must not be very straightforward. (21% "Proficient", 35% "Basic" in 2019)

https://nces.ed.gov/programs/coe/indicator/cnc

Also, "The Distribution User Skills, Worse than You Think" https://news.ycombinator.com/item?id=36620608

It's not even just math. Over half of the US adult population reads below a sixth-grade level. Their science literacy is worse.

No details but it's related to Pascal triangles? So it involves pricing financial instruments, seems like a safe guess...

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