[seqfan] Re: n-partitions of sum of powers of 0..n-1

[Ron Hardin]

The trailing 2's followed by 1 are


 All solutions for n=3 k=1  
..0....1..
..1....1..
..2....1..
..
All solutions for n=5 k=2  
..2....0..
..2....1..
..2....2..
..3....3..
..3....4..
..
All solutions for n=7 k=4  
..1....0..
..4....1..
..4....2..
..4....3..
..4....4..
..5....5..
..5....6..
..
All solutions for n=11 k=6  
..0....0..
..1....1..
..2....2..
..2....3..
..2....4..
..4....5..
..7....6..
..8....7..
..9....8..
..9....9..
..9...10..
..

rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: Max Alekseyev <maxale at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, August 24, 2012 4:30:15 PM
> Subject: [seqfan] Re: n-partitions of sum of powers of 0..n-1
> 
> Ron,
> In many rows the last non-1 equals 2.
> Can you check what other  solution this 2 counts?
> Do these other solutions show any pattern across the  rows?
> Max
> 
> On Fri, Aug 24, 2012 at 8:17 PM, Ron Hardin <rhhardin at att.net> wrote:
> > Where the  infinite row of 1's will begin, vs n?
> > (1..n gives a similar problem, if  I get to it)
> >
> > T(n,k)=Number of nondecreasing arrays of 0..n-1  integers with the sum of 
>their k
> > powers equal to  sum(i^k,i=0..n-1)
> >
> > Table starts
> >  ........1......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
> >  ........1......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1.1..
> >  ........2......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1....
> >  ........5......1....1...1.1.1.1.1.1.1.1.1.1.1.1......
> >  .......12......2....1...1.1.1.1.1.1.1.1.1.1.1........
> >  .......32......4....1...1.1.1.1.1.1.1.1.1.1..........
> >  .......94.....14....3...2.1.1.1.1.1.1.1..............
> >  ......289.....37....8...3.1.1.1.1.1.1................
> >  ......910....105...18...6.1.1.1.1.1..................
> >  .....2934....309...42..12.1.1.1.1....................
> >  .....9686....939..100..24.1.2.1......................
> >  ....32540...2903..265..63.2.2........................
> >  ...110780...8865..775.164.7..........................
> >  ...381676..28163.2241.424............................
> >  ..1328980..90648.6709................................
> >  ..4669367.297615.....................................
> >  .16535154............................................
> >
> > All  solutions for n=8 k=3
> > ..0....0....1....0....1....2....1....0..
> >  ..0....1....1....1....4....3....2....0..
> >  ..2....1....1....2....4....4....2....0..
> >  ..4....4....2....3....4....4....3....1..
> >  ..4....5....5....4....5....4....3....2..
> >  ..6....5....6....5....5....5....3....6..
> >  ..6....5....6....6....5....6....7....6..
> >  ..6....7....6....7....6....6....7....7..
> >
> >
> >  rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
> >
> >  _______________________________________________
> >
> > Seqfan Mailing  list - http://list.seqfan.eu/
> 
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