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 A182210 Triangle T(n,k) = floor(k*(n+1)/(k+1)), 1 <= k <= n. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). LINKS Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened FORMULA T(n,k) = floor(k(n+1)/(k+1)). EXAMPLE 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, MAPLE seq(seq(floor(k*(n+1)/(k+1)), k=1..n), n=1..15); MATHEMATICA Flatten[Table[Floor[k*(n+1)/(k+1)], {n, 0, 20}, {k, n}]] (* Harvey P. Dale, Jul 21 2015 *) PROG (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 CROSSREFS A004523(n+1) = T(n,2). Sequence in context: A342739 A137734 A352627 * A078705 A346018 A050331 Adjacent sequences: A182207 A182208 A182209 * A182211 A182212 A182213 KEYWORD nonn,nice,easy,tabl,look AUTHOR Dennis P. Walsh, Apr 18 2012 STATUS approved

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Last modified February 3 18:43 EST 2023. Contains 360044 sequences. (Running on oeis4.)