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

Author

Clark Kimberling

Keywords

• nonn

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

Examples

			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]
]
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..9938 (First 80 stages)

Crossrefs

The first row is A030777.

Cf. A030717.

Programs

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