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A030778
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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.
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10
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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)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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]
]
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PROG
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(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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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