A030777 The first 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, 1, 2, 1, 3, 1, 3, 6, 2, 5, 1, 1, 7, 4, 6, 1, 3, 2, 1, 8, 5, 9, 1, 1, 2, 4, 4, 2, 10, 7, 12, 1, 1, 2, 2, 4, 5, 5, 5, 11, 10, 15, 1, 2, 1, 3, 3, 3, 5, 6, 9, 7, 12, 13, 18, 1, 2, 1, 4, 2, 4, 5, 4, 7, 8, 11, 8, 16, 15, 21, 1, 2, 1, 4, 2, 5, 4, 5, 6, 7, 9, 9, 13, 12

Offset

1,1

Comments

The length of the first row after stage k is 1, 2, 4, 7, 10, 15, 22, 31, 42, 55, 70, 87, 106, ... - Peter Kagey, Apr 09 2020

Links

Peter Kagey, Table of n, a(n) for n = 1..9939 (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[0]
end # Peter Kagey, Apr 09 2020

Crossrefs

The second row is A030778.

Cf. A030717.

Sequence in context: A157520 A325116 A227339 * A353375 A056595 A160097

Adjacent sequences: A030774 A030775 A030776 * A030778 A030779 A030780

Keyword

nonn

Author

Clark Kimberling

Status

approved