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%I #46 Nov 18 2022 09:08:32
%S 1,1,2,2,1,3,2,3,3,1,4,3,3,4,3,5,1,5,3,6,2,1,6,4,7,2,2,1,7,6,7,3,2,2,
%T 1,8,8,8,3,2,3,3,8,9,11,3,2,3,3,3,8,10,15,3,2,3,3,4,1,1,10,11,18,4,2,
%U 3,3,5,1,1,1,1,14,12,20,5,3,3,3,5,1,2,2,1
%N The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.
%C The clarifying comment that follows refers to the old name, which was: Row 1, where, at stage k>1, write i in row 1 and j in row 2, where i is the number of j's in row 1, for j=1,2,...,m, where m=max number in row 1 from stages 1 to k-1; state 1 is 1 in row 1.
%C Numbers j for which the count is 0 are omitted, cf. A333867 for the corresponding sequence where they are included. - _Sean A. Irvine_, Apr 08 2020
%H Seiichi Manyama, <a href="/A030717/b030717.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Sean A. Irvine)
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a030/A030717.java">Java program</a> (github)
%e First list begins:
%e 1;
%e 1;
%e 2;
%e 2, 1;
%e 3, 2;
%e 3, 3, 1;
%e 4, 3, 3;
%e 4, 3, 5, 1;
%e 5, 3, 6, 2, 1;
%e 6, 4, 7, 2, 2, 1;
%e 7, 6, 7, 3, 2, 2, 1;
%e 8, 8, 8, 3, 2, 3, 3;
%e 8, 9, 11, 3, 2, 3, 3, 3;
%t t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {25}];
%t DeleteCases[Flatten[t], 0] (* _Peter J. C. Moses_, Apr 09 2020 *)
%Y Cf. A030718 (2nd list), A030719 (row lengths), A006920.
%Y Cf. A030707 (repeatedly adds values and frequencies from both lists).
%Y Cf. A333867 (0 counts included, but not the counts of 0s).
%Y Cf. A030723, A030724, A030725, A030726, A358423, A358424, A358425.
%K nonn,tabf,nice
%O 1,3
%A _Clark Kimberling_
%E More terms from _Franklin T. Adams-Watters_, Dec 14 2006
%E Rolled back to original definition and data by _Sean A. Irvine_, Apr 08 2020
%E Name revised in line with A030777 by _Peter Munn_, Oct 11 2022
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