[seqfan] Re: a simple Partitions question
Don Reble
djr at nk.ca
Sat Mar 20 21:13:41 CET 2010
> 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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