cp's OEIS Frontend

A030717 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.

%I A030717 #52 Mar 04 2025 23:26:07
%S A030717 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 A030717 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 A030717 3,3,5,1,1,1,1,14,12,20,5,3,3,3,5,1,2,2,1
%N A030717 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 A030717 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 A030717 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 A030717 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 A030717 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a030/A030717.java">Java program</a> (github)
%e A030717 First list begins:
%e A030717   1;
%e A030717   1;
%e A030717   2;
%e A030717   2, 1;
%e A030717   3, 2;
%e A030717   3, 3,  1;
%e A030717   4, 3,  3;
%e A030717   4, 3,  5, 1;
%e A030717   5, 3,  6, 2, 1;
%e A030717   6, 4,  7, 2, 2, 1;
%e A030717   7, 6,  7, 3, 2, 2, 1;
%e A030717   8, 8,  8, 3, 2, 3, 3;
%e A030717   8, 9, 11, 3, 2, 3, 3, 3;
%t A030717 t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {25}];
%t A030717 DeleteCases[Flatten[t], 0]  (* _Peter J. C. Moses_, Apr 09 2020 *)
%Y A030717 Cf. A030718 (2nd list), A030719 (row lengths), A006920.
%Y A030717 Cf. A030707 (repeatedly adds values and frequencies from both lists).
%Y A030717 Cf. A333867 (0 counts included, but not the counts of 0s).
%Y A030717 Cf. A030723, A030724, A030725, A030726, A358423, A358424, A358425.
%K A030717 nonn,tabf,nice
%O A030717 1,3
%A A030717 _Clark Kimberling_
%E A030717 More terms from _Franklin T. Adams-Watters_, Dec 14 2006
%E A030717 Rolled back to original definition and data by _Sean A. Irvine_, Apr 08 2020
%E A030717 Name revised in line with A030777 by _Peter Munn_, Oct 11 2022