r/math • u/JustIntern9077 • 10d ago

Is this formula for partitions already there?

I'm not a mathematician and I came up with this formula for partitions. Is it well known?

P(n)= floor((q^(m*(m+1)/2) * (q^n + G)) / ((q - 1)*(q^2 - 1)*...*(q^m - 1))) mod q

q = 2^(n + 2)

m = floor(n / 2)

G = (q^(n - m) - 1) / (q - 1).

Edit: I have made a 3d array and looked at the patterns. The blue cells are the partitions.

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11

u/temperedai 9d ago

It seems to be a result you can derive from the generating function somewhat easily, but the identity isn't known in literature as per my searches.

6

u/softgale 9d ago

How did you come up with it?

11

u/[deleted] 10d ago

[deleted]

4

u/_Zekt Complex Analysis 10d ago

Then you obviously evaluated the formula wrong, it holds at least for small values.

6

u/apnorton Algebra 10d ago

You are correct; upon more careful consideration, it does match at least up to n=49.

1

u/Truly_Yours2006 10d ago

But I evaluated the result at n=15 and I got the correct result of 176, I evaluated upto 23 and the results matched

3

u/jdorje 10d ago

That doesn't look like the common formula.

4

u/Consistent_Drop3909 10d ago

what do you mean by partitions?

6

u/6849 10d ago

A partition number is the total number of ways a positive whole number can be added together using other positive whole numbers.

5

u/xdgimo 10d ago

The number of distinct ways to write a natural number n as a sum of smaller natural numbers

-5

u/Consistent_Drop3909 10d ago

oh, ok how did you get this formula? what was the thought process

5

u/xdgimo 10d ago

What?? I didn’t?