[seqfan] Re: A007051

Reinhard Zumkeller reinhard.zumkeller at gmail.com
Thu Dec 4 14:31:24 CET 2014


https://oeis.org/A049456
Triangle T(n,k) = denominator of fraction in k-th term of n-th row of
variant of Farey series. This is also Stern's diatomic array read by rows
(version 1).

I wonder why there is no xref concerning row sums.

Best,
Reinhard

2014-12-04 11:40 GMT+01:00 Antreas Hatzipolakis <anopolis72 at gmail.com>:

> Consider the initial sequence 1,1, Insert between any two neighbor terms
> their sum: 1, 1 --> 1, 2, 1 and again
> 1, 1 --> 1, 2, 1 -- > 1, 3, 2, 3, 1 --> 1, 4, 3, 5, 2, 5, 3, 4, 1 and so on
>
> Reference:
> http://www.artofproblemsolving.com/Forum/viewtopic.php?t=31810
>
> Let Sn be the sum of the elements of the n-th sequence (set) divided by 2:
> (S1 = (1+1)/ 2 = 1, S2 = (1+2+1)/2 = 2, S3 = (1+3+2+3+1)/2 = 5 ......)
>
> Sn : 1, 2, 5, 14, 41, ......
>
> It is the sequence A007051
>
> But I do not know if the above is already mentioned  in the COMMENTS
> of the sequence (probably yes, but it is somehow difficult to me to check
> !).
>
> APH
>
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