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 A030778 The second list after the following procedure: starting with a list [3] and an empty list, repeatedly add the distinct values in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list. 2
 3, 3, 1, 3, 2, 1, 3, 2, 1, 6, 5, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 15, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 18, 16, 15, 13, 12, 11, 10, 9, 8, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The length of the second row after stage k is 0, 1, 3, 6, 9, 14, 21, 30, 41, 54, 69, 86, 105, ... - Peter Kagey, Apr 09 2020 LINKS Peter Kagey, Table of n, a(n) for n = 1..9938 (First 80 stages) EXAMPLE Stage 1: [   [3],   [] ] Stage 2:   [3, 1],      [3] ] Stage 3: [   [3, 1, 2, 1],      [3, 3, 1] ] Stage 4: [   [3, 1, 2, 1, 3, 1, 3],      [3, 3, 1, 3, 2, 1] ] Stage 5: [   [3, 1, 2, 1, 3, 1, 3, 6, 2, 5],      [3, 3, 1, 3, 2, 1, 3, 2, 1] ] Stage 6: [   [3, 1, 2, 1, 3, 1, 3, 6, 2, 5, 1, 1, 7, 4, 6],      [3, 3, 1, 3, 2, 1, 3, 2, 1, 6, 5, 3, 2, 1] ] PROG (Ruby) def a030777_list(generations)     rows = [[3], []]     (2..generations).each do         new_additions = rows.flatten.uniq.sort.reverse.map do |j|             [rows.flatten.count(j), j]         end         rows = rows.zip(new_additions.transpose).map { |r, n| r + n }     end     rows[1] end # Peter Kagey, Apr 09 2020 CROSSREFS The first row is A030777. Cf. A030717. Sequence in context: A138114 A124330 A055177 * A324078 A068119 A039992 Adjacent sequences:  A030775 A030776 A030777 * A030779 A030780 A030781 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 28 04:30 EST 2022. Contains 350654 sequences. (Running on oeis4.)