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.

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

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

Clark Kimberling

Status

approved