[seqfan] Re: A061857
Antti Karttunen
antti.karttunen at gmail.com
Fri May 11 16:01:18 CEST 2012
On Thu, May 10, 2012 at 9:56 PM, <seqfan-request at list.seqfan.eu> wrote:
> Message: 4
> Date: 07 May 2012 13:35:07 -0700
> From: israel at math.ubc.ca
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] A061857
> Message-ID: <Prayer.1.3.4.1205071335070.83 at viol.math.ubc.ca>
> Content-Type: text/plain; format=flowed; charset=ISO-8859-1
>
> A061857 was just now referenced in math.stackexchange.com
>
> http://math.stackexchange.com/questions/142323/sequence-generation/142364
>
> This is described as "Triangle where the k-th item at n-th row (both
> starting from 1) tells in how many ways we can add 2 distinct integers from
> 1 to n, in such way that the sum is divisible by k."
>
> Since the sum of two distinct integers from 1 to n can be as much as 2n-1,
> I don't see why the n'th row shouldn't have 2n-1 entries.
> But in fact the n'th row of the table has only n entries.
> Thus e.g. the 6th row is given as
> 15, 6, 5, 3, 3, 2
> but I think it should be
> 15, 6, 5, 3, 3, 2, 3, 2, 2, 1, 1
>
> Robert Israel
> University of British Columbia
>
>
Sorry, I forgot to reply to Neil (and you) about this.
I will create a new square array, with 2n-1 non-zero entries on each
row (followed by an infinite
number of zeroes), from which A061857 is the lower triangular slice,
and utilizing your improved formula.
(Unless of course somebody has already done that...)
But this might take a week or two, as I'm very busy up to the next
Thursday at least.
Cheers,
Antti Karttunen
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