[seqfan] A007051

[Antreas Hatzipolakis]

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