A261897 Triangle read by rows: T(n,k) (1 <= k <= n+1) = number of sequences of length n, dominated by the squares, with entries from [0,k] and largest entry k.
1, 1, 1, 0, 2, 1, 0, 2, 3, 1, 0, 2, 5, 4, 1, 0, 0, 7, 9, 5, 1, 0, 0, 7, 16, 14, 6, 1, 0, 0, 7, 23, 30, 20, 7, 1, 0, 0, 7, 30, 53, 50, 27, 8, 1, 0, 0, 7, 37, 83, 103, 77, 35, 9, 1, 0, 0, 0, 44, 120, 186, 180, 112, 44, 10, 1, 0, 0, 0, 44, 164, 306, 366, 292, 156, 54, 11, 1
Offset: 0
Examples
Triangle begins: 1, 1,1, 0,2,1, 0,2,3,1, 0,2,5,4,1, 0,0,7,9,5,1, 0,0,7,16,14,6,1, 0,0,7,23,30,20,7,1, 0,0,7,30,53,50,27,8,1, 0,0,7,37,83,103,77,35,9,1, 0,0,0,44,120,186,180,112,44,10,1, 0,0,0,44,164,306,366,292,156,54,11,1, ...
Links
- Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
- L. Haddad and C. Helou, Finite Sequences Dominated by the Squares, Journal of Integer Sequences, Volume 18, 2015, Issue 1, Article 15.1.8.
Programs
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Haskell
a261897 n k = a261897_tabl !! n !! (k-1) a261897_row n = a261897_tabl !! n a261897_tabl = [1] : f 1 0 [1] where f t h xs | t <= (h + 1) ^ 2 = ys : f (t + 1) h ys | otherwise = ys' : f (t + 1) (h + 1) ys' where ys = zipWith (+) ([0] ++ xs) (xs ++ [0]) ys' = zipWith (+) ([0] ++ xs) (us ++ (0:vs) ++ [0]) (us, _:vs) = splitAt h xs -- Reinhard Zumkeller, Sep 06 2015
Comments