[seqfan] Re: Sums of n products of pairs of 0..k integers?
Ron Hardin
rhhardin at att.net
Mon Apr 15 14:49:54 CEST 2013
It seems not to be true above k=31
...
T(n,31)=961*n-222 for n>1
T(n,32)=1024*n-234 for n>2
...
and n>2 until at least k=130.
T(n,32) = 355 1813 2838 3862 4886 5910 6934 7958 8982 10006 11030 12054
first difference
1458 1025 1024 1024 1024 1024 1024 1024 1024 1024 1024
rhhardin at mindspring.com
rhhardin at att.net (either)
----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Sun, April 14, 2013 1:36:59 PM
> Subject: [seqfan] Re: Sums of n products of pairs of 0..k integers?
>
> n>2 should read n>1 throughout
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>
> ----- Original Message ----
> > From: Ron Hardin <rhhardin at att.net>
> > To: seqfan at list.seqfan.eu
> > Sent: Sun, April 14, 2013 12:36:17 PM
> > Subject: [seqfan] Sums of n products of pairs of 0..k integers?
> >
> > Question at end
> >
> > /tmp/dgu
> > T(n,k)=Number of distinct values of the sum of n products of two 0..k
> integers
> >
> > Table starts
> > ..2..4..7..10..15..19..26..31..37..43..54..60..73.81
> > ..3..8.16..27..42..59..81.105.134.167.203.241.285...
> > ..4.12.25..43..67..95.130.169.215.267.324.385.......
> > ..5.16.34..59..92.131.179.233.296.367.445...........
> > ..6.20.43..75.117.167.228.297.377.467...............
> > ..7.24.52..91.142.203.277.361.458...................
> > ..8.28.61.107.167.239.326.425.......................
> > ..9.32.70.123.192.275.375...........................
> > .10.36.79.139.217.311...............................
> > .11.40.88.155.242...................................
> >
> > Row 1 is A027384
> >
> > Empirical for column k (based on not very many points):
> > k=1: a(n) = 1*n + 1
> > k=2: a(n) = 4*n
> > k=3: a(n) = 9*n - 2
> > k=4: a(n) = 16*n - 5 for n>2
> > k=5: a(n) = 25*n - 8 for n>2
> > k=6: a(n) = 36*n - 13 for n>2
> > k=7: a(n) = 49*n - 17 for n>2
> > k=8: a(n) = 64*n - 23 for n>2
> > k=9: a(n) = 81*n - 28 for n>2
> > k=10: a(n) = 100*n - 33 for n>2
> > k=11: a(n) = 121*n - 39 for n>2
> > k=12: a(n) = 144*n - 47 for n>2
> > k=13: a(n) = 169*n - 53 for n>2
> >
> > Apparently after the second row, each additional product adds the full k^2
>to
>
>
> > the attained values.
> >
> > Is this obvious?
> >
> >
> >
> > rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>
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