# [seqfan] Re: In the vein of 103314

Allan Wechsler acwacw at gmail.com
Fri Dec 22 04:02:35 CET 2017

```It's just a question of what values of k you permit. In my post I permit
k=0; Chai Wah Wu starts with k=1.

But why truncate the table at a triangle? It makes perfect sense to ask,
for instance, how many distinct values can be obtained by adding 17 9th
roots of unity.

It's also intriguing that the 6th row differs from the "hex numbers" by
leading with 6 rather than 7, which makes me suspect that in seeking
formulae for these rows, we should be wary of "startup glitches" in the
first few entries.

On Thu, Dec 21, 2017 at 8:26 PM, Chai Wah Wu <cwwuieee at gmail.com> wrote:

> I think the first term of the n-th row should be n, as there are n distinct
> roots of unity.
> I got the following triangular table:
>
> 1
> 2, 3
> 3, 6, 10
> 4, 9, 16, 25
> 5, 15, 35, 70, 126
> 6, 19, 37, 61, 91, 127
> 7, 28, 84, 210, 462, 924, 1716
> 8, 33, 96, 225, 456, 833, 1408, 2241
> 9, 45, 163, 477, 1197, 2674, 5454, 10341, 18469
> 10, 51, 180, 501, 1131, 2221, 3951, 6531, 10201, 15231
> 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756, 352716
> 12, 73, 253, 661, 1441, 2773, 4873, 7993, 12421, 18481, 26533, 36973
>
> Chai Wah
>
> ----- Original message -----
> From: Max Alekseyev <maxale at gmail.com>
> Sent by: "SeqFan" <seqfan-bounces at list.seqfan.eu>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc:
> Subject: [seqfan] Re: In the vein of 103314
> Date: Thu, Dec 21, 2017 1:57 AM
>
> Robert - yes, I agree.
> It may be worth also to consider other number of terms in the sum, giving
> raise to the table:
> 1,
> 1, 3,
> 1, 4, 10,
> 1, 5, 15, 25,
> 1, 6, 21, 56, 126,
> 1, 7, 28, 64, 100, 127,
> 1, 8, 36, 120, 330, 792, 1716,
> 1, 9, 45, 165, 495, 825, 1365, 2241,
> 1, 10, 55, 220, 715, 2002, 5005, 9724, 18469,
>
> The proposed sequence forms the main diagonal in this table.
>
> Regards,
> Max
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```