A003316
David W. Wilson
wilson at aprisma.com
Fri Sep 7 16:31:36 CEST 2001
Olivier Gerard wrote:
>
> David, if you re read the definition you will understand it better:
>
> 1 = 1*1
> 3 = 2*1 + 1*1
> 12 = 3*1 + 4*2 + 1*1
> 55 = 4*1 + 6*3 + 16*2 + 1*1
> etc...
Precisely. I get a(4) = 55 whereas the current sequence has a(4) = 58.
So where does the 58 come from?
>
> etc...
>
> Olivier
>
> On Fri, Sep 07, 2001 at 09:29:52AM -0400, David W. Wilson wrote:
> >
> >
> > %N A003316 Sum of lengths of longest increasing subsequences of all permutations
> > of n elements.
> > %S A003316 1,3,12,58,335,2261,17465,152020,1473057,15730705,183571817,
> > %T A003316 2324298010,31737207026,464904410985,7272666016725,121007866402968
> >
> > When I classify permutations by longest increasing subsequence, I get
> >
> > n 1 2 3 4 5 6 7 perms sum
> > 1 1 1 1
> > 2 1 1 2 3
> > 3 1 4 1 6 12
> > 4 1 16 6 1 24 55
> > 5 1 69 41 8 1 120 299
> > 6 1 348 293 67 10 1 720 1900
> > 7 1 2016 2309 602 99 12 1 5040 13942
> >
> > My table is in agreement with A008304, but my sums are not in agreement
> > with A003316 above.
> >
More information about the SeqFan
mailing list