OFFSET
1,3
COMMENTS
LINKS
Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened
Sela Fried and Toufik Mansour, The total number of descents and levels in (cyclic) tensor words, Disc. Math. Lett. (2024) Vol. 13, 44-49. See p. 49.
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
AUTHOR
Dennis P. Walsh, Apr 18 2012
STATUS
approved