Problem 402

[Nadando]

Can I get confirmation that S(10) = 1972 is correct? I get 1936 using several different methods.

[TripleM]

It is

[albert]

I can't wrap my head around the exclusion of S(F1) from the sum.
As far as I can tell S(1) is perfectly well defined.
Do I miss something important here?
Groetjes Albert

[dugo]

How do you read this out loud?

Also, define S(N) as the sum of M(a, b, c) for all ...

[Marcus_Andrews]

Let N=3

S(3) =
M(1,1,1)+
M(1,1,2)+
M(1,1,3)+
M(1,2,1)+
M(1,2,2)+
M(1,2,3)+
...
M(3,3,1)+
M(3,3,2)+
M(3,3,3)

[ffff0]

I can't wrap my head around the exclusion of S(F1) from the sum.
As far as I can tell S(1) is perfectly well defined.
Do I miss something important here?
Groetjes Albert

I think it was excluded because F1=F2.

[thundre]

How do you read this out loud?

Also, define S(N) as the sum of M(a, b, c) for all ...

Most of what you quoted is plain English. You'd normally read the functions as "ess of enn" and "emm of ay bee see". But it's more precise when written. If I was transcribing this for a blind PE participant, I would say "ess parentheses enn close parentheses".

[dugo]

Thanks thundre. I never had classroom training in this kind of math, let alone in English. Parsing these problems in your head is a lot harder if you can't find the proper words.

[mctrafik]

So totally hate this problem. Want to get that badge for the latest five. This is my last chance. Only got two days left. Grr. Sleepless nights. Hate number theory.

I'm losing my mind here. 0.o <- is what I look like.. unless it's this 0(-_-)0...z...Z....ZZZ...ZZz for like five minutes, then back to 0.o.

Anyway, can someone confirm that sum of s of fib of k to k = 6 is 1399. Just want to make sure I'm not taking crazy pills here. So if the problem statement is restated as C(N) = Sum_{k = 2 ... N} S(Fib_k), then find C(1234567890123) mod 10⁹. I want to make sure C(6) = 1399

Also. I don't like this problem because after a couple of days I found the asymptotic answer. I can get you the first 9 digits but not the last Hell. I can't even find S(10000). I'm missing something here.

[ffff0]

I've got C(6)=1401=2+20+57+266+1056.

[mctrafik]

Hm... I was suspecting that S(1) = 2 as the case where a = b = c = 1. I get the same numbers as you then. Damn it. I was hoping I was getting something wrong. Just can't see the pattern. Sadness.

Thank you.

Edit: then I guess C(15) = 601,313,396? Again. Hoping I'm off because this number is more out of whack than the others. Also largest I can compute under a minute.

[ffff0]

C(15) is indeed 601313396.

I think it's not possible to find a pattern by looking at numbers. You have to work with formulas.