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A212954
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Array of Ramsey numbers R(n,k) (n >= 1, k >= 1) read by antidiagonals.
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4
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 9, 9, 5, 1, 1, 6, 14, 18, 14, 6, 1, 1, 7, 18, 25, 25, 18, 7, 1, 1, 8, 23
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OFFSET
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1,5
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COMMENTS
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Essentially the same as A059442, which is the main entry for these numbers.
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REFERENCES
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LINKS
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Stanislaw Radziszowski, Small Ramsey Numbers, The Electronic Journal of Combinatorics, Dynamic Surveys, DS1, Mar 3 2017.
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FORMULA
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R(r, 1) = R(1, r) = 1
R(r, 2) = R(2, r) = r
R(r, s) <= R(r-1, s) + R(r, s-1)
R(r, s) <= R(r-1, s) + R(r, s-1) - 1 if R(r-1, s) and R(r, s-1) are both even
R(r, r) <= 4 * R(r, r-2) + 2
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EXAMPLE
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The initial antidiagonals are:
1,
1, 1,
1, 2, 1,
1, 3, 3, 1,
1, 4, 6, 4, 1,
1, 5, 9, 9, 5, 1,
1, 6, 14, 18, 14, 6, 1,
1, 7, 18, 25, 25, 18, 7, 1,
1, 8, 23, ?, ?, ?, 23, 8, 1,
1, 9, 28, ?, ?, ?, ?, 28, 9, 1,
1, 10, 36, ?, ?, ?, ?, ?, 36, 10, 1,
...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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