# [seqfan] Re: a simple Partitions question

wouter meeussen wouter.meeussen at pandora.be
Sat Mar 20 22:49:46 CET 2010

```Ah, cute, that is!

W.
btw.  thus that mean that P357(n) increases on average as O(lg(n))?

----- Original Message -----
From: "Don Reble" <djr at nk.ca>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Saturday, March 20, 2010 9:13 PM
Subject: [seqfan] Re: a simple Partitions question

> > strict partitions of n into positive powers of 3, 5 and 7,
> > ... the count of such partitions, say P357(n), ... shows
> > surprising symmetry:
> > P357(n) = P357(2270-n) for n>84
>
>     You mean 2271-n.
>
>     It's symmetric because
> 2271 = 3^1+3^2+3^3+3^4+3^5+3^6 + 5^1+5^2+5^3+5^4 + 7^1+7^2+7^3
>     That is, all powers less than 2187 (=3^7) contribute.
>     So for any partition of n, with (2271-2187) < n < 2187,
>     there's a complimentary partition for 2271-n.
>
> --
> Don Reble  djr at nk.ca
>
>
>
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```