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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.
18
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
KEYWORD
nonn
STATUS
approved