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A182210
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Triangle T(n,k) = floor(k*(n+1)/(k+1)), 1 <= k <= n.
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1
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1, 1, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 4, 5, 3, 4, 5, 5, 5, 6, 4, 5, 6, 6, 6, 6, 7, 4, 6, 6, 7, 7, 7, 7, 8, 5, 6, 7, 8, 8, 8, 8, 8, 9, 5, 7, 8, 8, 9, 9, 9, 9, 9, 10, 6, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 6, 8, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 7, 9, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 7, 10, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 8, 10, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15
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OFFSET
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1,3
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COMMENTS
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T(n,k) is the maximum number of wins in a sequence of n games in which the longest winning streak is of length k.
T(n,k) generalizes the pattern found in sequence A004523 where A004523(n) = floor(2n/3).
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LINKS
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Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened
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FORMULA
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T(n,k) = floor(k(n+1)/(k+1)).
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EXAMPLE
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T(12,4) = 10 since 10 is the maximum number of wins in a 12-game sequence in which the longest winning streak is 4. One such sequence with 10 wins is WWWWLWWWWLWW.
The triangle T(n,k) begins
1,
1, 2,
2, 2, 3,
2, 3, 3, 4,
3, 4, 4, 4, 5,
3, 4, 5, 5, 5, 6,
4, 5, 6, 6, 6, 6, 7,
4, 6, 6, 7, 7, 7, 7, 8,
5, 6, 7, 8, 8, 8, 8, 8, 9,
5, 7, 8, 8, 9, 9, 9, 9, 9, 10,
6, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11,
6, 8, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12,
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MAPLE
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seq(seq(floor(k*(n+1)/(k+1)), k=1..n), n=1..15);
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MATHEMATICA
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Flatten[Table[Floor[k*(n+1)/(k+1)], {n, 0, 20}, {k, n}]] (* Harvey P. Dale, Jul 21 2015 *)
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PROG
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(Haskell)
a182210 n k = a182210_tabl !! (n-1) !! (k-1)
a182210_tabl = [[k*(n+1) `div` (k+1) | k <- [1..n]] | n <- [1..]]
-- Reinhard Zumkeller, Jul 08 2012
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CROSSREFS
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A004523(n+1) = T(n,2).
Sequence in context: A181630 A112310 A137734 * A078705 A050331 A259194
Adjacent sequences: A182207 A182208 A182209 * A182211 A182212 A182213
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KEYWORD
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nonn,nice,easy,tabl,look
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AUTHOR
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Dennis P. Walsh, Apr 18 2012
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STATUS
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approved
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